Teachers often use wrong analogies like the one who created a question, "If an orchestra of 15 members plays a Beethoven piece in 20 minutes, how long would it take a 30-member orchestra to play the same piece?", and expecting an answer of 10 minutes.
I mean if 15 of them start from the beginning and the other 15 start from the end and they meet at the middle of the song and then you slice half of it reverse and paste in an editing software then BOOM! It only took 5 minutes!
@@mynameiskaboBecause it’s the same piece. If the music is 20 minutes long it’s going to take the same amount of time to finish the piece regardless of how many people are playing it.
@@mynameiskabo if you karaoke to Taylor Swift's Love Story and it took you 4 minutes, then you do a duet with your friend for the same song, you still gonna sing for 4 minutes. It's simply the length of the song.
I know right - If an off by one error is acceptable to a maths teacher or in presh's case professor... damn home schooling looking like a good choice! (also a life long code monkey)
That's not off-by-one. That's a stops-vs-stretches problem. "fence-post error" might be more appropriate although "off-by-one" is a fencepost type scenario. Not all fruit are apples, though.
Wrong, it never said she was sawing off the board into equal pieces, after making the first cut in 10 minutes she gives up and just cuts the corner of the board making it only around 11 minutes to cut it into 3 pieces.
*me, looking at this year's model of gas can nozzle, trying to figure out the 13 steps I'm supposed to do with ONE HAND(other is supporting the can) in order to get it to actually pour since they are redesigned almost yearly, remembering how this headache was caused by someone worrying about spilling a few drops of gas, and how much easier it is to accomplish both pouring and not spilling with my +20 year old can that has a simple pour spout and air hole "You don't get out much, do you?"
Basically, it's a case of misidentifying the x in an algebraic equation. The teacher defined x as the number of pieces, when x is actually the number of cuts. So she started with 2x=10, when it was really x=10. This is a common problem with word problems, where people pay more attention to the numbers than the actual word problem itself.
It's kinda like those tests where you are told to follow the directions at the top of the worksheet and most people will just ignore the instructions and begin answering all the questions on the worksheet when the directions just say to write your name at the top of the page, answer quedtion 15, and then turn in the worksheet.
A relative taught probablitity theory at university, and when I spent time with them as a child, they would teach me (read: test me) on math riddles and what not tied to mathematics). It was fun and made the subject fun for me. In my then class when I was some years later, us student had to practice speaking in front of the class and our mathematics teacher told us to teach the class something associated with maths. I did a mathematical riddle and the teacher said it was too difficult for the class and told me I had failed the assignement. I didn’t like school back then because even when you tried you were told to not do as much and it killed the joy in learning. Love it at uni. and how you are allowed to not only speak but to think for yourself and debate and think outside of the box and. Grateful I didn’t lose my curiosity or law would not be in my future.
@@oz_jones Them (and the other forms of they) can be singular and singular they has existed since the 14th century. This sentence is a good example of singular they/them "Somebody left their umbrella in the office. Could you please let them know where they can get it?"
Damn, IDK what university you attend, but from what I've seen of them lately(based on video evidence) they don't exactly encourage debating or thinking critically about much of anything these days. You're lucky.
hey presh, i think it's great that a lot of your videos explore not just concepts in 'pure' mathematics, but also issues in maths *education*. the latter i think is not only more accessible to a wider audience but is also far more impactful to society through our primary and secondary school teachers. keep up the good work in this space!
I would not be so kind to give the teacher a break. It's one thing to make an off-by-one error. But the teacher should have had access to the official answers. Especially since the concept of requiring only one cut to turn the board into 2 pieces is the heart of the question. But that's not the only reason. If this was the result of an actually graded test, that means that either not enough students gave the right answer to make the teacher question theirs, or the teacher simply refused to reflect on their own answer. Neither case reflects well on the teacher.
@@neh1234There's a difference between respect and arrogance, the only teachers who never check the official answers are arrogant stuck up teachers who believe that they're right over the students because of some teachers degree, even professional experienced teachers (were I'm from anyway) still check the the official answers and do research cause they have humility and don't close their minds to those they deem inferior to them. It doesn't matter if your older, wiser, smarter, more qualified or better overall than others you can still be wrong and/or misunderstand something as basic math.
@neh1234 Not doing any verification is the main reason why people get trapped with one-off error answer. As a teacher, it is her duty to be aware of this type of error.
I would only give the teacher a break if they admitted their mistake when it was explained to them, and apologized to the student. Otherwise, they really have no business teaching anything to anyone.
@@Bashaka104Yes. OP is saying if the teacher wanted to use the reasoning they wanted, where 2x=10 and 3x=15, they would need to reword the question like this.
If she sawed it two times she would have 3 pieces. Board starts as a single, one piece. Teacher assumes board starts at zero and cutting it magically summons pieces out of thin air.
0:45 My brain literally broke after I heard that explanation. I was just so flabbergasted by this “teachers“ reasoning that I just could not even. I say that teacher gets an F. Seriously.
I think the worst thing a person can do is be unwilling to double-check their own work. Particularly in Math. I had many Math instructors who were exemplary. Rather than being bitter at being corrected, they seemed to actually really appreciate it.
This is pretty typical. Smart kids don't want to be teachers because school is boring and mostly a waste of time. Average kids want to be teachers because school is interesting. Many classes have several kids who are significantly smarter than the teacher.
Fam the way my brain cycled through both answers is something else. 1st I thought, "easy it's 20mins because it's double the time/cuts". But then I saw the numbers 2 and 3 and thought "wait no, it's a ratio" and I worked that out as 15mins. Then I thought "no, that's wrong. It's 10mins for 1 cut, so 20mins for 2 cuts! my 1st answer was right" And all this took place in like a minute.
I find it hilarious that you admit this in public...especially the length of time it took you. It should be dead obvious what the answer is, and only take seconds to recognize. I failed 8th grade general math, and I had the answer pretty well instantly. Of course, I failed because I didn't ever do homework...I could do the math just fine.
@@TheEudaemonicPlague I find it hilarious that you feel the need to put other people down for second guessing themselves, and for not being as good at something as you perceive yourself to be.
@@TheEudaemonicPlague Calm down, it's not that deep.😂😂😂 But good on you for feeling superior to me and boasting to people about how smart you think you are.👍🏾
I'm glad you took your time and solved the problem correctly. I have helped many kids improve their math. When you stop them guessing, they improve very fast. You have solved it. Go!
I remember when I took a critical thinking class at uni. One day, we were given several “Is this possible” questions, one of which was as follows. “There are 101 people in a room. Each person in the room has a different number of hairs on their head to everyone else. The person with the greatest number of hairs has 100. Is this possible?” Some students got very emotional trying to explain to the tutor that he was wrong, and that the situation is not possible. He then went on to make a distinction between “counting from one” and “counting from zero”. This was a bit of a life-changing moment for me in the way that I understood the world. It’s so weirdly mundane, but I think about that lesson often.
This teacher is a perfect example of someone who never understood and thought about topics, just learned them. He simply made the calculation with the time and wood pieces instead of time and the actual work done which is the amount of cuts. No critical thinking, just using the formula. When i was tutoring i always used sneaky questions like this. Makes the kids laugh, a bit angry sometimes, but in the end they not only improve in their classes but learn to think for themselves and ask critical questions. This is something that should be ruthlessly hammered in to ongoing teachers.
I always gave snarky answers to those questions, because teaching math is not supposed to be about trick questions. So in this case I'd write: it depends on the size of the cuts, among other things, but the answer you'd want me to write is 15.
As you are a maths teacher I shall re post my comment here for you. Its so Important to teach students when problems can be solved in different ways and when its appropriate to use certain methods. This simple maths questions is deceptive because using simple maths of ANY kind will result in an incorrect answer. As a senior person in industry I have to spend so much time UNTEACHING kids what they have learned incorrectly at school or university! You seem like one of the good ones though so I encourage you to give my analysis of this problem to the kids to mull over - show them that sometimes the obvious calculation problem is actually much more complex in the real world. my comment: This isn't just a MATH TEACHING fail, its a MATH fail. YOU ARE WRONG PRESH! - there is actually insufficient information to solve accurately. This is a systems analysis question - not a maths question - and it must be solved as such! Math with give you a WRONG answer! The job requires you to get a board from location 1(t1), get a saw from location 2(t2), travel to a work bench at location 3(t3) - then set up the work bench to do the cut(t4), then do the cut(t5), then put the tools away and deliver the cut wood (t6) Ie Total Time T = t1+ t2+ t3 + t4 + t5 + t6 whereas for problem 2 its: T = t1 + t2 + t3 + t4 + 2(t5)+Overheads + t6 so in reality its more likely to be about 11 minutes - depending on all the values. You are wrong, the student was wrong and the teacher was wrong - and my answer is only right if i have correctly assessed the problem - which given the lack of detail is unlikely. What you have really shown here is why we CANNOT use maths to solve most real world logistics issues. If we were to use maths to solve this question for a home depot or homebase shop where they cut wood to order it would result in incorrect assessment of the time and loss of money or safety fails.
I should clarify that I am not a real teacher as in teaching whole classes at school, I just tutored and helped kids struggling with their grades in a private institute while studying. Atm I work in accounting and also do a lot of work with new and young hires. Because of that I really loved your comment and especially your phrasing, I couldn't agree more. With this much experience and creative style of thinking I am sure there are a lot of young colleagues really appreciative of you. And I am also very glad for your comment because it called me out for being a fool as well. That "sneaky operating" I mentioned earlier includes deliberately taking a false stance in order to be called out as well. Discovering this kind of thinking for one self and teaching it to the younglings is one of the most important things I believe. Having 5-10 students gang up on you for being wrong, even though there are still another 2 or 3 different "right" answers in the room were always among my favourite moments. In the end the only right answer that everyone could agree on was, that there were no right or wrong answers to these questions, just different ways of thinking. That video reminded me of that and I couldn't resist to let my sneaky side out ^^ @jbird4478, students like you I always liked the most. Nothing better and faster than immediately getting a smug answer to your face when trying to form such a discussion. I hope that you got at least a few thumb ups or even high fives for your answers ^^
@@bigolbearthejammydodger6527lol. Not a maths question you say whilst using two mathematical formulas to demonstrate how to solve it. It is a maths question, but you have to know what model to apply. Also your model is wrong in different contexts. I’m standing here at my workbench with my saw in hand and my two boards with the places to cut already marked. I’m very untidy, so I never put my tools away and somebody else is waiting to deliver the wood.
@@bigolbearthejammydodger6527 The question is about the action of sawing a board, not obtaining a board and saw or doing any of the other preparatory work you have included. In short, you've made the mistake of not answering the question by overthinking it, perhaps deliberately lol. That's why many students fail to finish tests in the allotted time!
@@ObsidianParis a sport teacher would probably just get a piece of wood a saw and try it out in practice since sport teachers tend to be more physical and like to move
Technically saying "I watched seasons 5 to 11" could be interpreted as not having watched season 11. You could be saying you started at 5, then watched up until 11 which would mean you stopped after season 10. That would be 5,6,7,8,9,10 making it 6 seasons. Saying "I watched seasons 5 thru 11" would then tack on the 11th season making it 7.
It could be misinterpreted that way sure, and yes many people do easily make that mistake, but it WOULD be a misinterpretation. It’s easier to think smaller: 1-2 must be referring to both one and two, otherwise it would just be 1 or 2 respectively. Because who says you need to include 5 with the faulty reasoning… you “could” be referring to seasons 6, 7, 8, 9, 10, and 11; even 6,7,8,9,10 is fair game if you allow for boundary errors to be acceptable.
Lol glad somebody else pointed it out first. In the end it comes down to where you are from and what's most common for you. JACpotatos explained it the best but with it only being the word "to" its not exactly inclusive or exclusive 🤷♂️
Submission refused. I would. I would, and do, call a piece of wood of any size a stick. A stick with a hole in it, be it a knot hole, or a worm hole, or a drilled hole, or whatever, is a torus.
Does this make it more acceptable? Starting with a square or rectangular board, cut a circle (or any other 2-d shape) from the middle of the board, resulting in two pieces with one cut. If the next cut is from an outer edge to the hole in the middle, then there are still only two pieces after the second cut. A third outer-to-centre cut will result in three pieces. Edit: extending this silliness, cutting _n_ non-intersecting shapes from the interior of board will yield _n+1_ pieces. It is then possible to make _n_ further cuts without creating any more pieces, by first cutting from an edge to an interior hole, then cutting from the first hole to the next, and so on. The _n+1_ th additional cut would be from the last hole to an outer edge and would finally generate the _n+2_ th piece. I'm thinking of the hole cuts as being in a row, but I wonder of there's a pattern of holes and joining cuts which breaks this pattern without allowing joining cuts to intersect each other.
@@geraldgomes And the drawing in the margin depicting the board being cut is clearly not a square, so it is implied that the board is longer than wide, and is being cut at it's narrowest dimension
11:36 if the frog is in a 12 foot well, he would need to leap >12 feet before being free. On day 10 he leaps to the 12 foot mark, which is not >12. So he would slide back to the 10 foot mark and on day 11 he would be free.
I suspect a teacher who went straight from being educated to becoming the educator, with no 'real life' job experience in between. To me, that was instantly a practical concern regarding the amount of work involved so I focussed on the number of cuts required.
8:14 actually, that's not the best way to explain this one. If you watched seasons 5-11, that means out of 11 seasons, you didn't watch 4 of them (seasons 1-4). Therefore, if you take the total number of seasons, 11, and subtract the number of seasons not watched, 4, you get 11 - 4 = 7, which means you have watched 7 seasons.
Good point. There's also some variability in the interpretation of the phrase "5 to 11". You can argue that '5 through 11' means you watched the entire 11th season.
@Pokerjinx. I agree that the approach you've taken is a much more natural way of seeing the situation and understanding why the calculation must be done that way. 5 through 11 =/= 6 seasons.
That is a practical way to solve it but his way of explaining is still good because it visualized the cause of error. (It was by counting the difference and not including the starting point which is season 5)
fence post issues in computer programming are not always related to that. Beginner programmers are taught to remember that counting is inclusive where subtraction is not. eg, `seq 1..5` will produce 5 iterations, not 5-1 iterations.
@@jrstf I remember working on a program which mixed FORTRAN and C++, some indices were 0-based and some were 1-based. Debugging that monstrosity was a nightmare.
I would like to offer a variation to your last example. If the frog is only able to progress to the exact top of the well on day 10, then did he really get out of the well? If 12 ft was all that he could progress, then he would fall back to the 10 ft mark, and only be able to truly get out of the well on day 11. It's another variation of the "off-by-one" fallacy. Another example is to say on the expiration date of milk, milk goes bad, when in reality it is meant to say that the expiration date is the last day of good milk, before it expires. To apply it to the "frog in the well" example, you would need to first explain whether 12ft is the "expiration length" or is it the "length it expires." If it is the "expiration length" then it would take more than 12 ft to exit the well, and if it is the "length of expiration" it would only take a minimum of 12 ft to exit the well. Sorry, not trying to be picky, as the video does an excellent job of explaining this commonly misunderstood concept, and my critique is only to show a variation and not to say that anything said in the video was wrong :) Great video!
I somewhat agree with you. I think they were wrong too. On day 9 not 10, the frog jumps the last three feet to the twelve foot mark, and they contend that the frog was out at that point, having reached the top of the hole. If that's their stance then they mislead us and said it took 10 days.
How thick was the wood that it took 10 minutes to saw through? Was the saw blunt? The actual answer is 9 minutes to sharpen the saw, 1 minute to make one cut, therefore two cuts take 2 minutes.
There was nothing about sharpening a blade in the problem. Also, if you've ever used a handsaw, you know most of them don't go dull in just one cut, two cuts, three cuts, or even several more. I am a woodworker, and these are things I know a lot about. I had a hand saw like the one shown in this video for forty years, and it never went dull enough to need sharpening in all of that time.
@@l.clevelandmajor9931 there is also nothing in the question about size of wood, which would affect the length of time. The true answer is "question needs more details to provide accurate timescales"
bingo - this is not a maths question, its a systems analysis and workflow logistics question. using simple maths will give a wrong answer and teachers need to teach students when they can and when they cant use a simple calculation to get a meaningful answer. In this problem as presented there is NO WAY to get a meaningful answer to this question using just maths.
Nope. They spent their childhood and teens being an average/nerdy kid, without doing anything interesting like DIY projects, then cashed in on their lack of ambition and got a teaching degree. And this is where it got them. Yay.
No, actually all answers disconsider the fact that the board was submitted to a gravitational attraction of one piece to each other. Once the gravitational attraction ceases from one part another, the board can be cut slightly faster, so the true answer is approximately 19,9999998 minutes.
I would respectfully disagree. If it's taking 5mins to make a single cut, then I would argue that we are talking about someone who is a true professional, that delivers quality workmanship, a genuine master of the trade. It's a person that will measure twice, then twice more with two different tape measures before cutting once... ... but more to the point, gravity won't be providing any assistance to the cut as this is someone who has several clamps holding the board down as it bridges across two workbenches that are perfectly square and braced with each other and has( a saw guide that's calibrated to 0.00° down two-centres of the cut line and can be executed to level of delicate precision which hasn't been seen since the Egyptian pyramids.
Ah, I see the teacher's mistake. The experience from the first cut will speed up the second cut. However, the dulling of the saw will slow down the second cut, evening out the speed-up from the experience. The teacher forgot to take the dulling of the saw into account.
don't forget heat expansion. a thicker saw is more cumbersome to operate, so the heat expansion from having already made one cut will slow down the second cut.
The frog in the well threw me off...by one...of your correct answer, but the way I interpreted it the frog had to jump _out_ of the well, not just reach the top of it.
@@3057luis You're off by one, you're forgetting that on day 9, the frog _starts_ at 8 feet, then jumps to 11 feet and slides down to 9 feet. The frog doesn't start at 9 feet on day 9, it *ends up* at 9 feet on day 9.
@@MLennholm You are correct. In general, the frog ENDS each day at foot-mark N on day N. Specifically, he ends up at foot-mark 9 on day 9. But it does NOT take a full day for the frog to go up 3 feet. Puzzle says the frog advances 3 feet BY DAY. So, we can ESTIMATE that at the end of the 1st half of day 10, it reaches the edge of the hole. So, one answer is 9.5 days. Buuuut.... Technically, the frog can't grab the edge without being at least tiniest bit BEYOND the edge... which he cannot do because he can AT MOST only reach the 12-foot mark. So, poor froggie slides back down until he reaches the 10-foot mark at the end of the 10th day. So, on the **11th** day, he gets out. When? If (assuming the frog makes uniform progress...) he can go 3 feet during the 12 hours of daytime, then it would take him 2/3rds of 12 hrs, or 8 hrs, to go the last 2 feet, plus the tiniest bit past, so he can grab the edge and pull himself out. Thus, 10 days 8hrs(+) 😂
I could be the smart-alec-in-class on the well point and argue 11 days for the same reason I'd tell someone who said 12 was off by one on their thought -- the well is 12 feet deep, so on day 10, the frog makes it to the surface, but doesn't leap *clear*, it leapt *to* the height of the opening, so one more day to jump clear. (Maths as "starts at -12, +3 jump, -2 slide, must reach higher than 0 to escape")
This is one of the reasons I hated math on elementary/middle school I thought about 11 too, but these scenarios are always so weird, they require some imagination, but not complete imagination, or else you will be wrong and you will receive 80/100 while the smartie will receive a 100/100 and be praised by all school teachers...
I think they were wrong too. On day 9 not 10, the frog jumps the last three feet to the twelve foot mark, and they contend that the frog was out at that point, having reached the top of the hole. If that's their stance then they mislead us and said it took 10 days!
Potentially confusing, rather than confusing I'd say colloquial and below standard for a largely mathematics based entertainer where those symbols should have consistent meanings. Expressing this video's duration as 1.243 cuts is open to misinterpretation.
You can make it somehow work if you consider that you only need off cuts of a given dimension. I know this is not what the problem states, because into doesn’t mean that, but this would make the number of cuts equal to the number of pieces. This may be what the professor had in mind.
Agreed. It's not ideal. Too many people get the impression that the equals sign means "and the answer is" or "and the next step is", instead of meaning that the thing on the left is equal to the thing on the right I like to see maths as a world of facts that you can explore. You can follow the implications of those facts to find new facts, and investigate wherever you choose. Too many people treat it more like a set of procedures you're supposed to execute, often robotically. They see an equation like "x²=4" and they talk about how you're "supposed" to "answer" it, which is silly IMHO, because "x²=4” isn't even a question i feel like using the equals sign this way contributes to that kind of thinking. But then, that's always bothered me a little about Presh; he seems inclined towards that way of thinking about maths. For instance, he talks about PEMDAS as if it's an unalterable fundamental truth of mathematics, instead of a convention that we use to help us communicate mathematics
I'm not sure which is more embarrassing for the teacher: Claiming that the time needed was a constant multiplied by the amount of pieces you get rather than the amount of cuts you make or the statement "10=2"
I mean, 2 is basically 3 at this point and you gotta round up to the nearest even number, and 4 is just an awkward number so it's basically 5, but 5 is half of our base 10 counting system so it's a bit weird, and 6 is really just the new 7, but 7 is even more awkward, and 8 is just a bit too round, but 9 is basically 10 so this equation is correct
For the final one about the frog, I was thinking 12ft being the top, that’s not quite OUT of the well, meaning the frog would need another day. But I get the point
@@Erik_Danley I was wondering if reaching the ledge enables it to hold on to it and climb out, or if it needs to jump higher than the ledge to clear the hole. So, depending on that it takes one day more if it needs to jump higher than the rim to make it out.
First, the side of a well is vertical, the frog is going to return to the bottom after each jump that doesn't get it out. Second, since the frog is jumping vertical, it will never get over the edge, just above the edge, then fall right back to the bottom.
One could also take the philosophical approach that you can only ever turn one board into 2 boards. Now you have two new boards, and each one can be made into 2 even smaller boards.
But the question states that Marie *can* turn a board into pieces of a board - so whether you or I are capable of it is irrelevant. Marie has the ability to do so.
As a woodworker I can tell you that cutting a board that’s half as wide will not take half the time of the wider board. It’s way more than half, but less than the original. Each stroke of the saw cuts a certain depth. It’ll be closer to the original board time, as long as the saw can stay on the board for its entire stroke. Unless it’s a bandsaw or table saw… then maybe it’s half the time, not counting setup time, but the picture shown was of a handsaw.
This channel is wild. 😂 Sometimes I feel like watching a video about quantum physics is more understandable than what is shown here. Other times, like right now, I thinkk I am watching sesame Street. I love it ❤. Never change📚🤠😂
Many off-by-one errors can be easily avoided by simply counting the right thing: Fence posts: count the posts NOT the gaps Cutting logs: count the cuts NOT the pieces So, if the student showed his work (as students are usually directed): 2 pieces requires 1 cut 1 cut took 10 minutes 2 cuts takes 20 minutes 2 cuts will produce 3 pieces, as required Froggy: Day 1 achieves 3 feet (albeit, temporarily) (day 1) + (distance remaining)/(distance per day) = days required = 3 + (12 - 3 )/(3 - 2) = 10 In other words, consider the _max_ reached each day, not the outcome each day. Although this seems more or less the same as considering the last day in the sequence as the special case....often in math (particularly with infinite series!), one can't consider the final case nearly as easily as the first case.
In the fence one, if you need to build a straight fence 30 feet long and space fence posts every 3 feet: you could say you need 11 fence posts BUT that would be assuming that you can exceed the 30 feet length of the fence by the combined width of the fence posts, or also assuming every fence post has 0 width. So, if you need to build a straight fence strictly 30 feet long and space fence posts every 3 feet (36 inches), then you could use 10 fence posts that are 3.6 inches wide: (10 separators (the separation the fences represent) -1)*36 inches + (10 fences)*3.6 inches = 360 inches or 30 feet Given that fence posts in real life do come at around 3.5 inches in width, using 10 fence posts for this scenario would come just 1 inch short of 30 feet, compared to using 11 which would exceed the 30 feet length by 38.5 inches or around 3 feet :p
The calculation at 7:55 could actually be argued as incorrect for the wording of the question. The answer could be seen as 6 and not 7 because it says, "5 to 11" and not "5 through 11," because "to" can imply that it was watched to that point, meaning all episodes of seasons 5 to 10 were watched, but were stopped when they reached season 11, thus season 11 isn't counted. While saying "through" instead, implies that they watched all the way through said seasons.
@Kyrelel Yes, you are correct that my answer can be wrong, but it's not a definite wrong, because of the wording of the question; this is why my answer also can't be the only correct answer (this is why I worded my answer as a possible way to interpret the question and not the only definitive answer. I'm not saying that the video is wrong; just another way to interpret it). To put it differently, let's change "seasons" to hours. For example, you have 5pm to 11pm to turn in an assignment. If you turned it in at 10:59pm, it would be on time, but if it were turned in at 11:01pm, it would be late because you don't count the whole hour of 11pm as the turn in time, because it's "to" 11 and not through the hour of 11.
Yeah, part of the riddle specifically said the sliding back happens at night. So if it's at the top on _day_ 10, it wouldn't have a chance to slide back down because it could just hop away before night came.
MikeG. I think your interpretation is legitimate. Can the frog get out, if he has JUST reached 12 feet and will immediately slide back down if he does NOT get out? This is something that needs to be specified. If a real world situation was similar to this situation, it could go either way.
The last one is wrong. Assuming (for simplicity) that nights last for 12 hours, the time needed for the frog to get out is 10 x 12 + 9 x 12 = 228 hours = 9.5 days
Interesting option, but i think there is not enough information to assume that the frog take 12 hours to jump because is not specified. "Every Day" means just to the number of the Day in which the frog is regardless of the hour, so i think 10 days is more correct, but even if you assume that frog jumps at first hour of the day, the answer will be 9.25 days, since the daytime starts at 6:00 am.
For the frog in a well the answer could also be 11 days assuming the well is exactly 12 feet deep meaning he would not get out by reaching 12 feet but rather has to jump above that
Another (wrong) way of interpreting the problem is to imagine that you're cutting two smaller pieces off of a larger board in ten minutes. Then it would take 15 minutes to cut three small pieces off. The key here is that the problem states that she cut a board INTO two pieces, not that she cut two pieces off the board.
You have my like as an apology for being unable to bear finishing this video, at no fault of your own. Like, this problem shouldn't need an explanation, this teacher is simply awful at math.
This is referred to as the fence post problem. Example: If the distance between two fence posts is 10 feet, how many fence posts do you need to make a fence 30 feet long? Answer is clearly 4 posts, but if you don't think about the fact that *each end* needs a fence post, it's easy to just do 30 / 10 = 3.
@@Grizzly01-vr4pn Someone got enthusiastic about sharing knowledge and acted on it right away instead of waiting a while first? Unacceptable, better snark at them for it :P
I had a situation like that. The question was as follows: A ship is sailing due south. It turns to sail north east. Through how many degrees did the ship turn? The correct answer was listed as 45, with a diagram of the ship's travel path given as reasoning.
Just to be in the same page, I assume the actual answer to be 135 degree? Alternatively, 225 degrees if the captain aren't confident with doing a left turn a.k.a. port side. I would accept 45 if it's a car or the ship had a reverse gear.
@@whatisdis Where we diverge is that you're thinking of this as a test; and I'm thinking of it more like a puzzle. As a test there's some "right answer", but to get there, you have to make what I'll dub "reasonable assumptions". By contrast, as a puzzle, there's a thing that's being described accurately; to get there, you have to figure out what "reasonable assumptions" you're making are failing you. So to address your post, I'll describe one way to say what you're saying. Suppose I'm facing south; so my heading is 180. If I want to face northeast, I must change my heading to be 45. One way of doing that is to rotate clockwise by 225 degrees. Another way of doing that is to rotate counterclockwise by 135 degrees. By my reading of the OP here, we have a ship that is sailing due south; to me that describes a motion along a straight line. The ship then turns; and by my reading, to "turn" here means to deviate from a straight line. The way I'm reading this, the "answer" of 45 degrees is really just part of the "puzzle"; so we have the ship deviating from the straight line by 45 degrees. So by my reading, you are allowed two operations... to go in a straight line, and to deviate from going in a straight line. Your deviation from a straight line must be by the amount of 45 degrees. Using these two operations you somehow need to change your heading (assuming it's 180; aka your sailing due south is going forward) from 180 to 45. Mind you, this isn't exactly one I would put in puzzle books... but thinking about this as a puzzle may help you figure out what's going on here. I could draw a diagram! ;)
@@whatisdis Apologize if there's a duplicate reply... I think my last attempt didn't take. But to be on the same page, here's one way to think about what you're describing, with caveats. If I am facing south, my heading is 180 degrees. If I am facing northeast, my heading is 45 degrees. In almost but not quite every situation, I can change my heading by rotating. One of the not-quite-every-situations is consistent with my having a heading of 180. Assuming pun only slightly intended that I'm in a position to change my heading by rotating, and am facing south, then I can change my heading to northeast by rotating clockwise 225 degrees or rotating counterclockwise by 135 degrees. If however I'm in that situation where I can't change my heading by turning, then those operations don't matter... regardless of how much I turn, my heading will always be 180, and the only way to change that would be for me to _move_. We can talk about maps as well; if I have a map such that going east is right, west is left, north is up, and south is down, as is canonical; I can imagine my location and orientation on that map. Those rotations can be thought of as spinning on some point in the map. That special location where my rotation will not change my heading, on this kind of map, if it's even on the map, is probably not a point, but rather a line; by contrast, that same location if I'm standing on it will indeed be a point. The reason it's a line on the map is because the map of this sort has to behave weirdly; or phrased another way, it's related to the fact that we're dividing by cosine of 90 degrees which is 0, so it's a singularity. But I digress. What were we talking about? Oh right. A ship. Okay, so we have a ship. That ship is sailing due south. I can't find anything about its heading, but I don't think it matters; we could say we're sailing in reverse if we really want to, but in that case we're still sailing south, as that's what the thing says, so our heading would be 0 but we're sailing in the same direction as if we were going forward with a heading 180 anyway. That's complicated, and I don't think it matters (the problem isn't to _face_ northeast anyway; it's just to _sail_ northeast), so I suggest just imagining us sailing forward anyway. So again we're sailing due south. Choosing my words very, very carefully... so long as we sail due south, we'll be going in a straight line. But there's another thing that happens... we turn. To turn in my understanding means to deviate from a straight path. By my _puzzle_ brain reading the OP, I interpret "the correct answer" as yet another specification; thus, I just take it to heart that when it says the ship turns by 45 degrees, it does in fact deviate from a straight path by 45 degrees. And apparently we do that "to sail northeast". In my puzzle like mind world where everyone's a perfect logician and what not, if the captain says he's turning 45 degrees to sail northeast, I trust him, but that implies that somehow, you can deviate from this straight path described as going south by an amount of 45 degrees and wind up sailing northeast. So the big question is, is that possible? And surprising at it may sound... yes, it's possible. To summarize, here are the parameters. 1. We start sailing south. This is a straight path. 2. We deviate from this straight path by 45 degrees. 3. Given nothing else unspecified happens; i.e., that all we do is _turn_ 45 degrees, and _travel on straight paths_, we will wind up traveling northeast. Somehow. Yep. It can happen. Need a diagram? ;) If you disagree, I'm almost certain you're making at least one assumption that is wrong.
I remember my dad asking me a joke question as a kid going something like "If it takes a man 10 minutes to dig a hole, how long does it take him to dig half a hole." Not a hole half the size, but half a hole which, of course, isn't a thing. Another good trick question is "how many bananas can you put in an empty barrel?", the correct answer being 1 of course since after that it's not empty. I came up with a slightly different answer of "1, assuming you cannot put multiple in at exactly the same time." I used to love finding alternate answers to trick questions, looking at them from different angles. Another was the old "A peacock lays an egg at the top of a hill. The egg rolls down the hill towards a wall. What happens when it hits the wall?" The usual answer being nothing as a peacock doesn't lay eggs. I used to argue this was an invalid argument as the question already notes that the peacock has, somehow, laid the egg. While this is something we've never known a peacock to be able to do, the one in this question managed it. Funnily enough, people don't like it when you point out the flaws in their arguments. While these aren't "off-by-one" errors, they are examples of how we have to look at things on a deeper level than simple surface assumptions. It's a good piece of practice in early childhood for anyone who might eventually go on to a logic-oriented, or research-involving, field.
With a square board, with a first cut parallel to 1 (therefore 2) of the sides in 10 minutes, a second cut at right angles to the first cut can take anything from almost 0 to almost 10 minutes. The assumption is that the first cut bisects the square and so is halfway along a side. For a square which is s x s in size, you can vary the proportion between left and right sides from 0 to s, hence the infinite number of answers between 0 and 10 minutes! Other topological shapes are of course possible such as an annular ring (donut). I’m not going to hurt my brain trying to cut a Möbius strip lengthwise!! 😂
This also assumes all cuts are made at right angles. If you make a 45 degree cuts then through the center it could take just over 14 minutes to make the single cut, and over 21 if you include the second "half" cut as well. If you cut near the corners it might only take a minute or two to make two cuts and end up with three pieces.
@@nurmr and that it is a “thin laminar” to preclude any 3 dimensional cuts!! If it is thick, you can put a cut through the plane of the shape - you could have two identical pieces… think of cutting through a cube or other shape with height breadth and depth. The question didn’t say you couldn’t think in 3 dimensions (conversely it didn’t say you could). There is no limit to our imagination!
You've ignored the grain issue. If you have only one saw, one of your cuts will be made across the grain with a ripsaw, or with the grain with a crosscut saw. That could make the second cut take longer than the first, if it's even possible at all!
It took Marie 5 minutes to find the saw, and another 5 minutes to make one cut to cut the board into two pieces. She now has the saw and another board of the same size as the first board. It will take 5 minutes for each of two cuts to make three equal size pieces. Therefore, the correct answer is 10 minutes.
But after making the cuts she has to put the saw away. This takes another 5 minutes because she has to decide where to place the saw so it will take 5 minutes to find it the next time she wants to use it. So, the teacher was right --- 15 minutes!
Requires making assumptions not stated in the problem. If we need to account for setup and cleanup time the answer is underdetermined because we don't actually know how long that takes; we have one equation with two unknowns
@@johnburgess2084 No, her husband had been using the saw and forgot to put it away, so she had to search for it. Normally, the saw hangs right here next to where she saws logs.
@@benroberts2222 As has been explained by many before me, there are as many correct answers as there are assumptions that can be made to fill in the missing data. Is the second piece of wood the same size and shape as the first? Did she just clip off the corners of the second piece of wood? Was she tired after cutting the first piece of wood? The missing data precludes one correct answer. Therefore, the assumptions I make make my answer correct for those assumptions.
Well, let me add that it never said into 2/3 equal sized pieces. We can assume the third piece can be a little corner piece that takes a minute. @@benroberts2222
Oh this is funny. I had a cake problem in math class that I got “wrong” for the same logic by the teacher. The question was something like this. Joe has a cake that needs to feed 100 people, how many cuts does Joe need to make to get 100 pieces of cake. My answer was 18 cuts, 9 vertical and 9 horizontal. The teacher marked me wrong because 9x9 is 81 not 100. I challenged this and she insisted it was wrong. I asked the other kids in the class if they answered 18 and if so to raise their hand. About half raised their hands, then I asked them to put your hand down if you got it right. The only kids left were the ones the teacher didn’t like, including me. She didn’t hide the fact that she didn’t like us, and I challenged this with her again. She kicked me out of class, sent me to the office and I had even more fun there. Told the principal what had happened, I even had my test with me to show him. We went back to her class and she was dismissed while the principal fixed our papers. Found out a few of her favorite students got the wrong answers right even. We didn’t see her for 2 weeks. And I can’t say she treated me any better when she came back. The following school year I once again got her as a teacher and immediately had my schedule changed. When I took the sheet to her to sign she was surprised I didn’t want to be in her class again. I told her I didn’t feel like being beaten and abused again by her. Her husband was the Principal of my high school the following year and up to my graduation and he was pretty cool. I actually liked him.
8:14 you could just do one extra cut from 5 cuts or 6 pieces for 6 cutsfor18 minutes because the question doesn’t say they all have to be vertical or horizontal
Funnily enough once someone commented in one of your video saying that once teacher asked to solve this same question with different values and the teacher did the same mistake but when that person corrected the teacher, teacher's face was worth watching 😂😂😂😂
When I was trying to solve the answer through the thumbnail, I thought it said 20 minutes was wrong, so I went into the actual video and it turns out I was not wrong 😂
no, it isn't because a "board" can be assumed to be significantly longer than it's wide. this would mean the time for the second, smaller cut is completely unknown. it would make the question unanswerable.
6:16 I’m sorry but disagree that we should give the teacher a break. While we all do make this mistake at least once, it’s while we are still learning about elementary math problems. An actual math teacher in a school should know better.
Actual teachers can make mistakes, it is how they react that matters. My teachers encouraged us to point out mistakes in the homework and/or test. I've had cases where a caught error became a free answer for the class. I've also had teachers who refused to either budge or elaborate on why they think they're right, so there are still casers where your point still stands, we just don't know which way the pendulum swings on this issue.
Problem is, while 1 cut creates 2 pieces, we are not told the dimensions of the second board, just that it is “another board”. So we are missing information. Assuming the second board is the same size as the first, it would be 10+10=20.
Unless the board is in the shape of a pizza😅 If cutting a pizza into two pieces takes 10 seconds, how long would it take to cut a similar sized pizza into 3 pieces?
@@RickyMaveety The dimensions may be assumed from the 2nd picture and the statement of “equal effort”. Now if the pictures are not to part of the puzzle, then perhaps. But I go upon what I see, not what I imagine.
Because the teacher took 10 minutes and divided by 2 to get 5, then multiplied by 3 to to get 15. Not realizing it is not the number of pieces but the number of cuts.
8:00 I would argue that they said 5 TO 11, they never said they watched all of season 11 just that they've gotten to it, in this case 6 is the right answer
I have to say on the last example the correct answer is 9 not 10 as the frog jumped out of the hole on the 9th day ,dosent fall back 2 feet and never even gets to day 10 11:58
Aha! You're off by one! If the well is 12 feet deep, and the frog jump from 9 feet that day he only reach 12 feet which just exactly at the same height as the well which realistically resulting he can't jump out of the well, so the frog need a day more to jump off.
4:25 - yeah creative, but not the same board and cut as the original question. Marie won't be able to cut half her post longways, but, if she did then the long cut would take much longer and the answer would be greater than 15mins (in fact it'd be greater than 20 mins)
The teacher was counting pieces, the student correctly counted cuts.
You are right.
yup, you got it in a nutshell
I agree. This is not an "off by one error". It's an error in using the wrong unit rate.
Precisely.
Yes
Makes me think perhaps you could also count jobs - Marie can be working just as fast per job, so 10 mins for the other one too
Ugh, I always hate it when I have to wait 5 minutes so my board is in 1 piece
Yeah, it is annoying indeed. In the morning I have to wait 40 minutes for my table to be in a single piece before I can have breakfast
Lol
ONE PIECE
@@Haus_360 yesterday, my desk was extra hard, and it took me a whole hour to cut it into one whole piece. Ugh, so annoying!
Damn, and when I wait 0 minutes and it goes to limbo
Teachers often use wrong analogies like the one who created a question, "If an orchestra of 15 members plays a Beethoven piece in 20 minutes, how long would it take a 30-member orchestra to play the same piece?", and expecting an answer of 10 minutes.
I mean if 15 of them start from the beginning and the other 15 start from the end and they meet at the middle of the song and then you slice half of it reverse and paste in an editing software then BOOM! It only took 5 minutes!
wait, why is it not 10 minutes?
@@mynameiskaboBecause it’s the same piece. If the music is 20 minutes long it’s going to take the same amount of time to finish the piece regardless of how many people are playing it.
@@mynameiskabo if you karaoke to Taylor Swift's Love Story and it took you 4 minutes, then you do a duet with your friend for the same song, you still gonna sing for 4 minutes. It's simply the length of the song.
@@NessieNice oh, now i understand it
I was a software engineer for 20 years, 19 of which were spent correcting off-by-one errors 😂
I know right - If an off by one error is acceptable to a maths teacher or in presh's case professor... damn home schooling looking like a good choice! (also a life long code monkey)
Are you sure it wasn't 20?
So you were a software engineer for 19 years, 20 of which were spent making off by one errors?
@@igrim4777 Come to think of it...hmm... let's see...
That's not off-by-one. That's a stops-vs-stretches problem. "fence-post error" might be more appropriate although "off-by-one" is a fencepost type scenario. Not all fruit are apples, though.
WRONG WRONG WRONG
Marie is ambidextrous, so with a saw in each hand, it only takes her 10 minutes to cut the board into 3 pieces.
Nah but it does say that they work just as fast, and using 2 hands is working twice as fast
Taking into account strength imbalances and bilateral deficit tho it should actually be closer to 15ish lol
@@fgvcosmic6752yeah but you can argue the hands are working just as fast, no one said how many hands were working.
Yayyyyyyy🎉🎉🎉🎉🎉
Wrong, it never said she was sawing off the board into equal pieces, after making the first cut in 10 minutes she gives up and just cuts the corner of the board making it only around 11 minutes to cut it into 3 pieces.
OMG ... this has to be the most monumental case of overthinking I've seen in years.
Absolutely
*me, looking at this year's model of gas can nozzle, trying to figure out the 13 steps I'm supposed to do with ONE HAND(other is supporting the can) in order to get it to actually pour since they are redesigned almost yearly, remembering how this headache was caused by someone worrying about spilling a few drops of gas, and how much easier it is to accomplish both pouring and not spilling with my +20 year old can that has a simple pour spout and air hole
"You don't get out much, do you?"
Poor teacher, didnt know that you get 1 free piece at the start
ONE PIECE!??!??!
@@ayhanrashidi1563 THE ONE PIECE IS REAL!!!!!!
yes, @@ayhanrashidi1563 ONE PIECE!!!
@@ayhanrashidi1563it was always real!
meanwhile me out here thinking "10 mins to get 2 pieces, 20 mins to get three, and a spare one" because you're cutting two different boards.
Basically, it's a case of misidentifying the x in an algebraic equation. The teacher defined x as the number of pieces, when x is actually the number of cuts. So she started with 2x=10, when it was really x=10. This is a common problem with word problems, where people pay more attention to the numbers than the actual word problem itself.
Yep. That's the crucial idea to keep in mind here.
well, you can use X as teacher used too, but he never realized that she STARTS with one piece (ONE PIECE IS REAL)
It's called critical thinking and many people never learn it.
It's kinda like those tests where you are told to follow the directions at the top of the worksheet and most people will just ignore the instructions and begin answering all the questions on the worksheet when the directions just say to write your name at the top of the page, answer quedtion 15, and then turn in the worksheet.
@@redstonewarrior0152 Especially when some of the directions say flap your arms like a bird or other silly stuff.
A relative taught probablitity theory at university, and when I spent time with them as a child, they would teach me (read: test me) on math riddles and what not tied to mathematics). It was fun and made the subject fun for me. In my then class when I was some years later, us student had to practice speaking in front of the class and our mathematics teacher told us to teach the class something associated with maths. I did a mathematical riddle and the teacher said it was too difficult for the class and told me I had failed the assignement. I didn’t like school back then because even when you tried you were told to not do as much and it killed the joy in learning. Love it at uni. and how you are allowed to not only speak but to think for yourself and debate and think outside of the box and. Grateful I didn’t lose my curiosity or law would not be in my future.
Relative: singular
Them: plural
@@oz_jones Them (and the other forms of they) can be singular and singular they has existed since the 14th century. This sentence is a good example of singular they/them "Somebody left their umbrella in the office. Could you please let them know where they can get it?"
Somebody who actually belongs in uni, bravo
Damn, IDK what university you attend, but from what I've seen of them lately(based on video evidence) they don't exactly encourage debating or thinking critically about much of anything these days. You're lucky.
Law, why not do something useful with your intelligence and curiosity.
Law is manipulation and deception, you are better than that!
That must be one really dense board for it to take 10 minutes to saw it into 2 pieces
They forgot to say the board was 18 inches wide and 4 inches thick.
Dense board and an even denser teacher!
or marie is shockingly terrible at using a saw
The teacher was told to use a hand saw and she thought that's what a hacksaw was ... 24 tooth blade at that.
Try cutting a sheet of plywood/OSB/MDF (or any other wooden board) in half with a hand saw and see how long it takes.
This is like that old riddle "If you're running in a race and pass the person in third place, which place are you now in?"
Indeterminate. On a circuit race the persons in first and second places could each pass the person in third place without changing race order.
@@igrim4777fine then. You're running on a straight track. Happy?
@@igrim4777 They wouldn't pass them, they would lap them them
It depends on which direction you're going 😁
@@deept3215 that’s a semantic argument, and a bad argument too. Lapping someone involves passing them *by definition*
hey presh, i think it's great that a lot of your videos explore not just concepts in 'pure' mathematics, but also issues in maths *education*. the latter i think is not only more accessible to a wider audience but is also far more impactful to society through our primary and secondary school teachers. keep up the good work in this space!
Why is the text on your comment black, in the dark mode?
Edit: Nevermind, It was probably a bug.
There are two difficult problems in computer science: naming things, cache invalidation, and off by one errors.
And you just got one off!
@@l.clevelandmajor9931 that's the joke
that is going in my memes channel for the work discord!
good one
If there are two things I’m not good at, it’s counting.
I would not be so kind to give the teacher a break. It's one thing to make an off-by-one error. But the teacher should have had access to the official answers. Especially since the concept of requiring only one cut to turn the board into 2 pieces is the heart of the question. But that's not the only reason. If this was the result of an actually graded test, that means that either not enough students gave the right answer to make the teacher question theirs, or the teacher simply refused to reflect on their own answer. Neither case reflects well on the teacher.
To be fair, I don't think any self respecting adult would feel the need to check on the official answers for such an elementary question.
@@neh1234and that's the reason why so many adults keep being posted on r/confidentialIncorrect.
@@neh1234There's a difference between respect and arrogance, the only teachers who never check the official answers are arrogant stuck up teachers who believe that they're right over the students because of some teachers degree, even professional experienced teachers (were I'm from anyway) still check the the official answers and do research cause they have humility and don't close their minds to those they deem inferior to them. It doesn't matter if your older, wiser, smarter, more qualified or better overall than others you can still be wrong and/or misunderstand something as basic math.
@neh1234 Not doing any verification is the main reason why people get trapped with one-off error answer. As a teacher, it is her duty to be aware of this type of error.
I would only give the teacher a break if they admitted their mistake when it was explained to them, and apologized to the student. Otherwise, they really have no business teaching anything to anyone.
Instead "It took Marie 10 minutes to saw a board 2 times. How long would it take her to sae another board 3 times?"
But she only sawed it 1 and then 2 times
You are counting pieces
@@Bashaka104Yes. OP is saying if the teacher wanted to use the reasoning they wanted, where 2x=10 and 3x=15, they would need to reword the question like this.
so op should learn how to type
If she sawed it two times she would have 3 pieces. Board starts as a single, one piece. Teacher assumes board starts at zero and cutting it magically summons pieces out of thin air.
or changing the word "board" to "cake" fixes it too
0:45 My brain literally broke after I heard that explanation. I was just so flabbergasted by this “teachers“ reasoning that I just could not even. I say that teacher gets an F. Seriously.
I think the worst thing a person can do is be unwilling to double-check their own work. Particularly in Math.
I had many Math instructors who were exemplary. Rather than being bitter at being corrected, they seemed to actually really appreciate it.
This is pretty typical. Smart kids don't want to be teachers because school is boring and mostly a waste of time. Average kids want to be teachers because school is interesting.
Many classes have several kids who are significantly smarter than the teacher.
that's literally how i solved it lmao
Except for the fact in this case the teachers actually right 😂
@@grimmspectrum1547Have u tried thinking
Fam the way my brain cycled through both answers is something else.
1st I thought, "easy it's 20mins because it's double the time/cuts".
But then I saw the numbers 2 and 3 and thought "wait no, it's a ratio" and I worked that out as 15mins.
Then I thought "no, that's wrong. It's 10mins for 1 cut, so 20mins for 2 cuts! my 1st answer was right"
And all this took place in like a minute.
I find it hilarious that you admit this in public...especially the length of time it took you. It should be dead obvious what the answer is, and only take seconds to recognize. I failed 8th grade general math, and I had the answer pretty well instantly. Of course, I failed because I didn't ever do homework...I could do the math just fine.
@@TheEudaemonicPlague I find it hilarious that you feel the need to put other people down for second guessing themselves, and for not being as good at something as you perceive yourself to be.
@@TheEudaemonicPlague Calm down, it's not that deep.😂😂😂
But good on you for feeling superior to me and boasting to people about how smart you think you are.👍🏾
I'm glad you took your time and solved the problem correctly. I have helped many kids improve their math. When you stop them guessing, they improve very fast. You have solved it. Go!
@@TheEudaemonicPlague who asked
I remember when I took a critical thinking class at uni. One day, we were given several “Is this possible” questions, one of which was as follows. “There are 101 people in a room. Each person in the room has a different number of hairs on their head to everyone else. The person with the greatest number of hairs has 100. Is this possible?” Some students got very emotional trying to explain to the tutor that he was wrong, and that the situation is not possible. He then went on to make a distinction between “counting from one” and “counting from zero”. This was a bit of a life-changing moment for me in the way that I understood the world. It’s so weirdly mundane, but I think about that lesson often.
This teacher is a perfect example of someone who never understood and thought about topics, just learned them.
He simply made the calculation with the time and wood pieces instead of time and the actual work done which is the amount of cuts. No critical thinking, just using the formula.
When i was tutoring i always used sneaky questions like this. Makes the kids laugh, a bit angry sometimes, but in the end they not only improve in their classes but learn to think for themselves and ask critical questions.
This is something that should be ruthlessly hammered in to ongoing teachers.
I always gave snarky answers to those questions, because teaching math is not supposed to be about trick questions. So in this case I'd write: it depends on the size of the cuts, among other things, but the answer you'd want me to write is 15.
As you are a maths teacher I shall re post my comment here for you.
Its so Important to teach students when problems can be solved in different ways and when its appropriate to use certain methods. This simple maths questions is deceptive because using simple maths of ANY kind will result in an incorrect answer.
As a senior person in industry I have to spend so much time UNTEACHING kids what they have learned incorrectly at school or university!
You seem like one of the good ones though so I encourage you to give my analysis of this problem to the kids to mull over - show them that sometimes the obvious calculation problem is actually much more complex in the real world.
my comment:
This isn't just a MATH TEACHING fail, its a MATH fail.
YOU ARE WRONG PRESH! - there is actually insufficient information to solve accurately.
This is a systems analysis question - not a maths question - and it must be solved as such! Math with give you a WRONG answer!
The job requires you to get a board from location 1(t1), get a saw from location 2(t2), travel to a work bench at location 3(t3) - then set up the work bench to do the cut(t4), then do the cut(t5), then put the tools away and deliver the cut wood (t6)
Ie Total Time T = t1+ t2+ t3 + t4 + t5 + t6
whereas for problem 2 its: T = t1 + t2 + t3 + t4 + 2(t5)+Overheads + t6
so in reality its more likely to be about 11 minutes - depending on all the values.
You are wrong, the student was wrong and the teacher was wrong - and my answer is only right if i have correctly assessed the problem - which given the lack of detail is unlikely. What you have really shown here is why we CANNOT use maths to solve most real world logistics issues.
If we were to use maths to solve this question for a home depot or homebase shop where they cut wood to order it would result in incorrect assessment of the time and loss of money or safety fails.
I should clarify that I am not a real teacher as in teaching whole classes at school, I just tutored and helped kids struggling with their grades in a private institute while studying. Atm I work in accounting and also do a lot of work with new and young hires. Because of that I really loved your comment and especially your phrasing, I couldn't agree more. With this much experience and creative style of thinking I am sure there are a lot of young colleagues really appreciative of you.
And I am also very glad for your comment because it called me out for being a fool as well.
That "sneaky operating" I mentioned earlier includes deliberately taking a false stance in order to be called out as well. Discovering this kind of thinking for one self and teaching it to the younglings is one of the most important things I believe.
Having 5-10 students gang up on you for being wrong, even though there are still another 2 or 3 different "right" answers in the room were always among my favourite moments. In the end the only right answer that everyone could agree on was, that there were no right or wrong answers to these questions, just different ways of thinking.
That video reminded me of that and I couldn't resist to let my sneaky side out ^^
@jbird4478, students like you I always liked the most. Nothing better and faster than immediately getting a smug answer to your face when trying to form such a discussion.
I hope that you got at least a few thumb ups or even high fives for your answers ^^
@@bigolbearthejammydodger6527lol. Not a maths question you say whilst using two mathematical formulas to demonstrate how to solve it.
It is a maths question, but you have to know what model to apply. Also your model is wrong in different contexts. I’m standing here at my workbench with my saw in hand and my two boards with the places to cut already marked. I’m very untidy, so I never put my tools away and somebody else is waiting to deliver the wood.
@@bigolbearthejammydodger6527 The question is about the action of sawing a board, not obtaining a board and saw or doing any of the other preparatory work you have included. In short, you've made the mistake of not answering the question by overthinking it, perhaps deliberately lol. That's why many students fail to finish tests in the allotted time!
Wouldn't surprise me at all.... here in Australia we now have sports teachers teaching maths....
Was it due to budget cuts? But now that professional sports is run by analytics, maybe the sports teachers will be good math teachers ;)
Physics for us😭😭
They bring us teachers who don’t know how to convert between gram and kilogram 💀💀💀
Ironicaly enough, a sport teacher would probably have come to the correct solution from the beginning…
@@ObsidianParis a sport teacher would probably just get a piece of wood a saw and try it out in practice since sport teachers tend to be more physical and like to move
@@MindYourDecisionsIn Gr 7 the gym teacher was also the math teacher AND the health teacher, when I was 12.
Technically saying "I watched seasons 5 to 11" could be interpreted as not having watched season 11. You could be saying you started at 5, then watched up until 11 which would mean you stopped after season 10. That would be 5,6,7,8,9,10 making it 6 seasons. Saying "I watched seasons 5 thru 11" would then tack on the 11th season making it 7.
Touché
It could be misinterpreted that way sure, and yes many people do easily make that mistake, but it WOULD be a misinterpretation.
It’s easier to think smaller: 1-2 must be referring to both one and two, otherwise it would just be 1 or 2 respectively. Because who says you need to include 5 with the faulty reasoning… you “could” be referring to seasons 6, 7, 8, 9, 10, and 11; even 6,7,8,9,10 is fair game if you allow for boundary errors to be acceptable.
@@jakemartinez6894to be fair, it's also just poorly worded. It'd make more sense to say you watched "x through y" or "x up to/until y"
I came here to make the same comment. The "to" vs "thru". To definitely implies "up to" and is not a misinterpretation.
Lol glad somebody else pointed it out first. In the end it comes down to where you are from and what's most common for you. JACpotatos explained it the best but with it only being the word "to" its not exactly inclusive or exclusive 🤷♂️
So it turns out that the shape of the wood board is ambiguous and the piece in the drawings was a lie.
It just wasnt to scale
Nah it turns out some people tend to missinterpret questions by omitting some words used
literally the funny cheese question
Dude! Check out the picture of the board that is being cut (next to the question). Nothing ambiguous.
@@wessanders4566 But it's "not to scale"
I submit that there is no one anywhere who would consider a torus to be a “board.”
If the board was a square, then the teacher could be right. But the dimensions of the board were not specified and a board is usually not a square.
Submission refused.
I would.
I would, and do, call a piece of wood of any size a stick.
A stick with a hole in it, be it a knot hole, or a worm hole, or a drilled hole, or whatever, is a torus.
Does this make it more acceptable? Starting with a square or rectangular board, cut a circle (or any other 2-d shape) from the middle of the board, resulting in two pieces with one cut.
If the next cut is from an outer edge to the hole in the middle, then there are still only two pieces after the second cut. A third outer-to-centre cut will result in three pieces.
Edit: extending this silliness, cutting _n_ non-intersecting shapes from the interior of board will yield _n+1_ pieces. It is then possible to make _n_ further cuts without creating any more pieces, by first cutting from an edge to an interior hole, then cutting from the first hole to the next, and so on. The _n+1_ th additional cut would be from the last hole to an outer edge and would finally generate the _n+2_ th piece.
I'm thinking of the hole cuts as being in a row, but I wonder of there's a pattern of holes and joining cuts which breaks this pattern without allowing joining cuts to intersect each other.
@@geraldgomes And the drawing in the margin depicting the board being cut is clearly not a square, so it is implied that the board is longer than wide, and is being cut at it's narrowest dimension
@@jeremyashford2145 Jeremy, you need education...a torus is not just something with a hole in it. Look it up, learn something.
Me taking 5 minutes to materialize a board of wood:
11:36 if the frog is in a 12 foot well, he would need to leap >12 feet before being free. On day 10 he leaps to the 12 foot mark, which is not >12. So he would slide back to the 10 foot mark and on day 11 he would be free.
1:03 Teacher proving they've never picked up a board in their life or even seen carpentry done.
I suspect a teacher who went straight from being educated to becoming the educator, with no 'real life' job experience in between. To me, that was instantly a practical concern regarding the amount of work involved so I focussed on the number of cuts required.
@@brianstuntman4368 Even then, did they not do any kind of woodwork in high school?
they seem to have never done anything in their life ngl
never cooked, never did handicrafts, never ate a kitkat, never shared a bar of chocolate...
And I don't think any of you three succeeded in math because the teacher is right
How@@grimmspectrum1547
6:32 As an AMC competitor, I can attest to this that I made almost a hundred off by one errors in my history of practice problems
8:14 actually, that's not the best way to explain this one. If you watched seasons 5-11, that means out of 11 seasons, you didn't watch 4 of them (seasons 1-4). Therefore, if you take the total number of seasons, 11, and subtract the number of seasons not watched, 4, you get 11 - 4 = 7, which means you have watched 7 seasons.
Good point. There's also some variability in the interpretation of the phrase "5 to 11". You can argue that '5 through 11' means you watched the entire 11th season.
@Pokerjinx.
I agree that the approach you've taken is a much more natural way of seeing the situation and understanding why the calculation must be done that way.
5 through 11 =/= 6 seasons.
That is a practical way to solve it but his way of explaining is still good because it visualized the cause of error. (It was by counting the difference and not including the starting point which is season 5)
In computers, we start an index with 0, so at 15, we have a count of 16. I'm very familiar with the off by one issue.
fence post issues in computer programming are not always related to that. Beginner programmers are taught to remember that counting is inclusive where subtraction is not. eg, `seq 1..5` will produce 5 iterations, not 5-1 iterations.
Not me, I'm a FORTRAN programmer.
@@jrstf I remember working on a program which mixed FORTRAN and C++, some indices were 0-based and some were 1-based. Debugging that monstrosity was a nightmare.
I would like to offer a variation to your last example. If the frog is only able to progress to the exact top of the well on day 10, then did he really get out of the well? If 12 ft was all that he could progress, then he would fall back to the 10 ft mark, and only be able to truly get out of the well on day 11. It's another variation of the "off-by-one" fallacy. Another example is to say on the expiration date of milk, milk goes bad, when in reality it is meant to say that the expiration date is the last day of good milk, before it expires. To apply it to the "frog in the well" example, you would need to first explain whether 12ft is the "expiration length" or is it the "length it expires." If it is the "expiration length" then it would take more than 12 ft to exit the well, and if it is the "length of expiration" it would only take a minimum of 12 ft to exit the well. Sorry, not trying to be picky, as the video does an excellent job of explaining this commonly misunderstood concept, and my critique is only to show a variation and not to say that anything said in the video was wrong :) Great video!
I somewhat agree with you. I think they were wrong too. On day 9 not 10, the frog jumps the last three feet to the twelve foot mark, and they contend that the frog was out at that point, having reached the top of the hole. If that's their stance then they mislead us and said it took 10 days.
How thick was the wood that it took 10 minutes to saw through? Was the saw blunt? The actual answer is 9 minutes to sharpen the saw, 1 minute to make one cut, therefore two cuts take 2 minutes.
There was nothing about sharpening a blade in the problem. Also, if you've ever used a handsaw, you know most of them don't go dull in just one cut, two cuts, three cuts, or even several more. I am a woodworker, and these are things I know a lot about. I had a hand saw like the one shown in this video for forty years, and it never went dull enough to need sharpening in all of that time.
@@l.clevelandmajor9931 there is also nothing in the question about size of wood, which would affect the length of time. The true answer is "question needs more details to provide accurate timescales"
bingo - this is not a maths question, its a systems analysis and workflow logistics question. using simple maths will give a wrong answer and teachers need to teach students when they can and when they cant use a simple calculation to get a meaningful answer. In this problem as presented there is NO WAY to get a meaningful answer to this question using just maths.
"Marie needs to stop skipping pull day."
actually its 11 minutes because she needs to sharpen the saw first
that teacher has never cut a board in half.
Nope. They spent their childhood and teens being an average/nerdy kid, without doing anything interesting like DIY projects, then cashed in on their lack of ambition and got a teaching degree. And this is where it got them. Yay.
Yeah, they don't have time since they're always waiting to cut a board to one piece
The only thing they've ever cut in half is - something something, rhythm of a joke.
Nobody said half, just two pieces.
@@davelordy.....is a large cake, half for now and half for later coz we all know they’ll be fat with blue hair and a nose piercing
Imagine getting confused by your own question
No, actually all answers disconsider the fact that the board was submitted to a gravitational attraction of one piece to each other. Once the gravitational attraction ceases from one part another, the board can be cut slightly faster, so the true answer is approximately 19,9999998 minutes.
I would respectfully disagree. If it's taking 5mins to make a single cut, then I would argue that we are talking about someone who is a true professional, that delivers quality workmanship, a genuine master of the trade. It's a person that will measure twice, then twice more with two different tape measures before cutting once...
... but more to the point, gravity won't be providing any assistance to the cut as this is someone who has several clamps holding the board down as it bridges across two workbenches that are perfectly square and braced with each other and has( a saw guide that's calibrated to 0.00° down two-centres of the cut line and can be executed to level of delicate precision which hasn't been seen since the Egyptian pyramids.
Ah, I see the teacher's mistake. The experience from the first cut will speed up the second cut. However, the dulling of the saw will slow down the second cut, evening out the speed-up from the experience. The teacher forgot to take the dulling of the saw into account.
i love this comment section lol
don't forget heat expansion. a thicker saw is more cumbersome to operate, so the heat expansion from having already made one cut will slow down the second cut.
A saw won't dull after one cut
THE TEACHER OFFICALLY HAD NO LEGAL RIGHTS TO MARK THE STUDENT'S ANSWER AS WRONG WHEN THE STUDENT'S ANSWER WAS RIGHT.
The frog in the well threw me off...by one...of your correct answer, but the way I interpreted it the frog had to jump _out_ of the well, not just reach the top of it.
The frog would have to jump more than 3 feet to get out on day 10, but it is only almost out. On day 11 it would be able to jump out of the hole.
@brandonfeingold4116 yes, that was my reasoning too.
@@3057luis Day 9 = 11 ft
@@3057luis You're off by one, you're forgetting that on day 9, the frog _starts_ at 8 feet, then jumps to 11 feet and slides down to 9 feet. The frog doesn't start at 9 feet on day 9, it *ends up* at 9 feet on day 9.
@@MLennholm You are correct.
In general, the frog ENDS each day at foot-mark N on day N. Specifically, he ends up at foot-mark 9 on day 9. But it does NOT take a full day for the frog to go up 3 feet. Puzzle says the frog advances 3 feet BY DAY. So, we can ESTIMATE that at the end of the 1st half of day 10, it reaches the edge of the hole. So, one answer is 9.5 days.
Buuuut.... Technically, the frog can't grab the edge without being at least tiniest bit BEYOND the edge... which he cannot do because he can AT MOST only reach the 12-foot mark. So, poor froggie slides back down until he reaches the 10-foot mark at the end of the 10th day. So, on the **11th** day, he gets out. When? If (assuming the frog makes uniform progress...) he can go 3 feet during the 12 hours of daytime, then it would take him 2/3rds of 12 hrs, or 8 hrs, to go the last 2 feet, plus the tiniest bit past, so he can grab the edge and pull himself out. Thus, 10 days 8hrs(+) 😂
I could be the smart-alec-in-class on the well point and argue 11 days for the same reason I'd tell someone who said 12 was off by one on their thought -- the well is 12 feet deep, so on day 10, the frog makes it to the surface, but doesn't leap *clear*, it leapt *to* the height of the opening, so one more day to jump clear. (Maths as "starts at -12, +3 jump, -2 slide, must reach higher than 0 to escape")
That actually crossed my mind as well.
This is one of the reasons I hated math on elementary/middle school
I thought about 11 too, but these scenarios are always so weird, they require some imagination, but not complete imagination, or else you will be wrong and you will receive 80/100 while the smartie will receive a 100/100 and be praised by all school teachers...
I think they were wrong too. On day 9 not 10, the frog jumps the last three feet to the twelve foot mark, and they contend that the frog was out at that point, having reached the top of the hole. If that's their stance then they mislead us and said it took 10 days!
Teacher: you will use these in real life
Also the teacher:
It's confusing when you equate the units "cuts", "pieces" and "minutes." An implication symbol would be more appropriate than an equal sign.
Potentially confusing, rather than confusing I'd say colloquial and below standard for a largely mathematics based entertainer where those symbols should have consistent meanings. Expressing this video's duration as 1.243 cuts is open to misinterpretation.
You can make it somehow work if you consider that you only need off cuts of a given dimension. I know this is not what the problem states, because into doesn’t mean that, but this would make the number of cuts equal to the number of pieces. This may be what the professor had in mind.
Agreed. It's not ideal. Too many people get the impression that the equals sign means "and the answer is" or "and the next step is", instead of meaning that the thing on the left is equal to the thing on the right
I like to see maths as a world of facts that you can explore. You can follow the implications of those facts to find new facts, and investigate wherever you choose. Too many people treat it more like a set of procedures you're supposed to execute, often robotically. They see an equation like "x²=4" and they talk about how you're "supposed" to "answer" it, which is silly IMHO, because "x²=4” isn't even a question
i feel like using the equals sign this way contributes to that kind of thinking. But then, that's always bothered me a little about Presh; he seems inclined towards that way of thinking about maths. For instance, he talks about PEMDAS as if it's an unalterable fundamental truth of mathematics, instead of a convention that we use to help us communicate mathematics
@@igrim4777i can feel myself getting smarter reading this...
@@douglaswolfen7820, also, it should be PE{DM}{AS}. Multiplication and division have equal precedence. Addition and subtraction have equal precedence.
I'm not sure which is more embarrassing for the teacher: Claiming that the time needed was a constant multiplied by the amount of pieces you get rather than the amount of cuts you make or the statement "10=2"
I mean, 2 is basically 3 at this point and you gotta round up to the nearest even number, and 4 is just an awkward number so it's basically 5, but 5 is half of our base 10 counting system so it's a bit weird, and 6 is really just the new 7, but 7 is even more awkward, and 8 is just a bit too round, but 9 is basically 10 so this equation is correct
1:50 THE ONE PIECE IS REAL!
Yes zoro!!
For the final one about the frog, I was thinking 12ft being the top, that’s not quite OUT of the well, meaning the frog would need another day. But I get the point
@@Erik_Danley I was wondering if reaching the ledge enables it to hold on to it and climb out, or if it needs to jump higher than the ledge to clear the hole. So, depending on that it takes one day more if it needs to jump higher than the rim to make it out.
It is in a super position. You should not look at the frog on day 9.
yeah that's the problem with contrived problems such as that one.
not carefully worded enough to have a single reasonable solution.
First, the side of a well is vertical, the frog is going to return to the bottom after each jump that doesn't get it out. Second, since the frog is jumping vertical, it will never get over the edge, just above the edge, then fall right back to the bottom.
Well, assuming a perfectly spherical frog...
5 minutes to go find the saw, 5 minutes for each cut. Makes sense to me.
No need to go find the saw again, so still 10 min then. :-)
I spent SO long looking at the thumbnail thinking you were saying the teacher was correct and was scratching my head
One could also take the philosophical approach that you can only ever turn one board into 2 boards. Now you have two new boards, and each one can be made into 2 even smaller boards.
-Or you can never cut a board into two, because if you cut a board, you have two HALF boards :D
But the question states that Marie *can* turn a board into pieces of a board - so whether you or I are capable of it is irrelevant. Marie has the ability to do so.
@@bobagorof Spoilsport! Ruining a perfectly good philosophical discussion :D
As a woodworker I can tell you that cutting a board that’s half as wide will not take half the time of the wider board. It’s way more than half, but less than the original. Each stroke of the saw cuts a certain depth. It’ll be closer to the original board time, as long as the saw can stay on the board for its entire stroke. Unless it’s a bandsaw or table saw… then maybe it’s half the time, not counting setup time, but the picture shown was of a handsaw.
2:24 say that again..
xD
God damn it
THE ONE PIECE IS REAAAAAAAAAAAAL
NOO
Thank god someone else thought it 😂😂
This channel is wild. 😂 Sometimes I feel like watching a video about quantum physics is more understandable than what is shown here. Other times, like right now, I thinkk I am watching sesame Street. I love it ❤. Never change📚🤠😂
Many off-by-one errors can be easily avoided by simply counting the right thing:
Fence posts: count the posts NOT the gaps
Cutting logs: count the cuts NOT the pieces
So, if the student showed his work (as students are usually directed):
2 pieces requires 1 cut
1 cut took 10 minutes
2 cuts takes 20 minutes
2 cuts will produce 3 pieces, as required
Froggy:
Day 1 achieves 3 feet (albeit, temporarily)
(day 1) + (distance remaining)/(distance per day) = days required
= 3 + (12 - 3 )/(3 - 2) = 10
In other words, consider the _max_ reached each day, not the outcome each day.
Although this seems more or less the same as considering the last day in the sequence as the special case....often in math (particularly with infinite series!), one can't consider the final case nearly as easily as the first case.
In the fence one, if you need to build a straight fence 30 feet long and space fence posts every 3 feet: you could say you need 11 fence posts BUT that would be assuming that you can exceed the 30 feet length of the fence by the combined width of the fence posts, or also assuming every fence post has 0 width. So, if you need to build a straight fence strictly 30 feet long and space fence posts every 3 feet (36 inches), then you could use 10 fence posts that are 3.6 inches wide:
(10 separators (the separation the fences represent) -1)*36 inches + (10 fences)*3.6 inches = 360 inches or 30 feet
Given that fence posts in real life do come at around 3.5 inches in width, using 10 fence posts for this scenario would come just 1 inch short of 30 feet, compared to using 11 which would exceed the 30 feet length by 38.5 inches or around 3 feet :p
Exactly. Anyone who had built their own fence has figured this out
It's 15 minutes because she already found the saw.
🗿
Those first 10 minutes also included the time it took to find the board? And now that the sawer knows where to get another…?
The little laugh you tried to stifle at 4:45 made this video.
Just recently found this channel and I already love it so much
In the teacher's defense, the clip at 1:19 of the person sawing the board, really felt like it was 20 minutes long!
But 20 minutes was the student's answer...
@@thatonefrenchguy937 Technically you're right, but it felt like an eternity, lol
1:08 eventually everyone saw 😆
Good catch. I aspire to be you.
IOW I saw what you did there.
"But eventually everyone saw" At first I thought wow that is the most implausible statement I have heard all month. Then I SAW what you did there 😉
These are the type of counting issues programmers have to learn to solve quickly and accurately... I know from experience.
The calculation at 7:55 could actually be argued as incorrect for the wording of the question. The answer could be seen as 6 and not 7 because it says, "5 to 11" and not "5 through 11," because "to" can imply that it was watched to that point, meaning all episodes of seasons 5 to 10 were watched, but were stopped when they reached season 11, thus season 11 isn't counted. While saying "through" instead, implies that they watched all the way through said seasons.
It could be argued that way .. but it would be wrong.
@Kyrelel Yes, you are correct that my answer can be wrong, but it's not a definite wrong, because of the wording of the question; this is why my answer also can't be the only correct answer (this is why I worded my answer as a possible way to interpret the question and not the only definitive answer. I'm not saying that the video is wrong; just another way to interpret it).
To put it differently, let's change "seasons" to hours. For example, you have 5pm to 11pm to turn in an assignment. If you turned it in at 10:59pm, it would be on time, but if it were turned in at 11:01pm, it would be late because you don't count the whole hour of 11pm as the turn in time, because it's "to" 11 and not through the hour of 11.
@@Kyrelel To and until can be used synonymously, maybe english isn't your first language, you shouldn't try to correct people.
Hahaha - "If you never made an off by one mistake - I am sure your estimate is off by one"
That was brilliant!
I had the frog riddle wrong, but not because of being off by one . . . for some reason, I assumed the frog would still slide back down at 12 feet. 🤣
Indeed, reaching the top is not the same as getting out. To get out it needs to have jump distance left, after reaching the top.
Yeah, part of the riddle specifically said the sliding back happens at night. So if it's at the top on _day_ 10, it wouldn't have a chance to slide back down because it could just hop away before night came.
Yes me too! That is ambigious question.
MikeG. I think your interpretation is legitimate.
Can the frog get out, if he has JUST reached 12 feet and will immediately slide back down if he does NOT get out? This is something that needs to be specified.
If a real world situation was similar to this situation, it could go either way.
@@UTU49 Yes, may be the distance should not be a multiple of the climbing distance.
The last one is wrong. Assuming (for simplicity) that nights last for 12 hours, the time needed for the frog to get out is 10 x 12 + 9 x 12 = 228 hours = 9.5 days
Interesting option, but i think there is not enough information to assume that the frog take 12 hours to jump because is not specified. "Every Day" means just to the number of the Day in which the frog is regardless of the hour, so i think 10 days is more correct, but even if you assume that frog jumps at first hour of the day, the answer will be 9.25 days, since the daytime starts at 6:00 am.
For the frog in a well the answer could also be 11 days assuming the well is exactly 12 feet deep meaning he would not get out by reaching 12 feet but rather has to jump above that
OTOH it says the frog “can” jump 1 foot each day, not that it does. It might never jump, not even trying to escape from the well!
Obviously if it takes 10 minutes to make a single cut in a board, you should go to the hardware store and buy a new saw with sharp teeth.
Another (wrong) way of interpreting the problem is to imagine that you're cutting two smaller pieces off of a larger board in ten minutes. Then it would take 15 minutes to cut three small pieces off. The key here is that the problem states that she cut a board INTO two pieces, not that she cut two pieces off the board.
You have my like as an apology for being unable to bear finishing this video, at no fault of your own. Like, this problem shouldn't need an explanation, this teacher is simply awful at math.
This is referred to as the fence post problem. Example:
If the distance between two fence posts is 10 feet, how many fence posts do you need to make a fence 30 feet long?
Answer is clearly 4 posts, but if you don't think about the fact that *each end* needs a fence post, it's easy to just do 30 / 10 = 3.
Didn't watch the video all the way through before commenting, eh?
@@Grizzly01-vr4pn Someone got enthusiastic about sharing knowledge and acted on it right away instead of waiting a while first? Unacceptable, better snark at them for it :P
@@ItsAsparageese Yep, that pretty much sums it up.
@@Grizzly01-vr4pn I'm sincerely sorry for you about your weird priorities
@@ItsAsparageese Don't be. You have no place being sorry for me nor judging any of my priorities. You deal with your own business.
I had a situation like that. The question was as follows:
A ship is sailing due south. It turns to sail north east. Through how many degrees did the ship turn?
The correct answer was listed as 45, with a diagram of the ship's travel path given as reasoning.
Ah, the backwards swimming ship. My favourite.
Not necessarily. Though I haven't seen this diagram, from the description, this is entirely possible and checks out, requiring only forward motion.
Just to be in the same page, I assume the actual answer to be 135 degree? Alternatively, 225 degrees if the captain aren't confident with doing a left turn a.k.a. port side.
I would accept 45 if it's a car or the ship had a reverse gear.
@@whatisdis Where we diverge is that you're thinking of this as a test; and I'm thinking of it more like a puzzle. As a test there's some "right answer", but to get there, you have to make what I'll dub "reasonable assumptions". By contrast, as a puzzle, there's a thing that's being described accurately; to get there, you have to figure out what "reasonable assumptions" you're making are failing you.
So to address your post, I'll describe one way to say what you're saying. Suppose I'm facing south; so my heading is 180. If I want to face northeast, I must change my heading to be 45. One way of doing that is to rotate clockwise by 225 degrees. Another way of doing that is to rotate counterclockwise by 135 degrees.
By my reading of the OP here, we have a ship that is sailing due south; to me that describes a motion along a straight line. The ship then turns; and by my reading, to "turn" here means to deviate from a straight line. The way I'm reading this, the "answer" of 45 degrees is really just part of the "puzzle"; so we have the ship deviating from the straight line by 45 degrees. So by my reading, you are allowed two operations... to go in a straight line, and to deviate from going in a straight line. Your deviation from a straight line must be by the amount of 45 degrees. Using these two operations you somehow need to change your heading (assuming it's 180; aka your sailing due south is going forward) from 180 to 45.
Mind you, this isn't exactly one I would put in puzzle books... but thinking about this as a puzzle may help you figure out what's going on here. I could draw a diagram! ;)
@@whatisdis Apologize if there's a duplicate reply... I think my last attempt didn't take.
But to be on the same page, here's one way to think about what you're describing, with caveats. If I am facing south, my heading is 180 degrees. If I am facing northeast, my heading is 45 degrees. In almost but not quite every situation, I can change my heading by rotating. One of the not-quite-every-situations is consistent with my having a heading of 180. Assuming pun only slightly intended that I'm in a position to change my heading by rotating, and am facing south, then I can change my heading to northeast by rotating clockwise 225 degrees or rotating counterclockwise by 135 degrees. If however I'm in that situation where I can't change my heading by turning, then those operations don't matter... regardless of how much I turn, my heading will always be 180, and the only way to change that would be for me to _move_. We can talk about maps as well; if I have a map such that going east is right, west is left, north is up, and south is down, as is canonical; I can imagine my location and orientation on that map. Those rotations can be thought of as spinning on some point in the map. That special location where my rotation will not change my heading, on this kind of map, if it's even on the map, is probably not a point, but rather a line; by contrast, that same location if I'm standing on it will indeed be a point. The reason it's a line on the map is because the map of this sort has to behave weirdly; or phrased another way, it's related to the fact that we're dividing by cosine of 90 degrees which is 0, so it's a singularity. But I digress. What were we talking about? Oh right. A ship.
Okay, so we have a ship. That ship is sailing due south. I can't find anything about its heading, but I don't think it matters; we could say we're sailing in reverse if we really want to, but in that case we're still sailing south, as that's what the thing says, so our heading would be 0 but we're sailing in the same direction as if we were going forward with a heading 180 anyway. That's complicated, and I don't think it matters (the problem isn't to _face_ northeast anyway; it's just to _sail_ northeast), so I suggest just imagining us sailing forward anyway.
So again we're sailing due south. Choosing my words very, very carefully... so long as we sail due south, we'll be going in a straight line. But there's another thing that happens... we turn. To turn in my understanding means to deviate from a straight path. By my _puzzle_ brain reading the OP, I interpret "the correct answer" as yet another specification; thus, I just take it to heart that when it says the ship turns by 45 degrees, it does in fact deviate from a straight path by 45 degrees. And apparently we do that "to sail northeast". In my puzzle like mind world where everyone's a perfect logician and what not, if the captain says he's turning 45 degrees to sail northeast, I trust him, but that implies that somehow, you can deviate from this straight path described as going south by an amount of 45 degrees and wind up sailing northeast. So the big question is, is that possible?
And surprising at it may sound... yes, it's possible. To summarize, here are the parameters. 1. We start sailing south. This is a straight path. 2. We deviate from this straight path by 45 degrees. 3. Given nothing else unspecified happens; i.e., that all we do is _turn_ 45 degrees, and _travel on straight paths_, we will wind up traveling northeast. Somehow. Yep. It can happen. Need a diagram? ;)
If you disagree, I'm almost certain you're making at least one assumption that is wrong.
I remember my dad asking me a joke question as a kid going something like "If it takes a man 10 minutes to dig a hole, how long does it take him to dig half a hole." Not a hole half the size, but half a hole which, of course, isn't a thing.
Another good trick question is "how many bananas can you put in an empty barrel?", the correct answer being 1 of course since after that it's not empty. I came up with a slightly different answer of "1, assuming you cannot put multiple in at exactly the same time."
I used to love finding alternate answers to trick questions, looking at them from different angles. Another was the old "A peacock lays an egg at the top of a hill. The egg rolls down the hill towards a wall. What happens when it hits the wall?" The usual answer being nothing as a peacock doesn't lay eggs. I used to argue this was an invalid argument as the question already notes that the peacock has, somehow, laid the egg. While this is something we've never known a peacock to be able to do, the one in this question managed it. Funnily enough, people don't like it when you point out the flaws in their arguments.
While these aren't "off-by-one" errors, they are examples of how we have to look at things on a deeper level than simple surface assumptions. It's a good piece of practice in early childhood for anyone who might eventually go on to a logic-oriented, or research-involving, field.
8:12 Or just do 11-4, since there's 4 seasons you haven't seen.
With a square board, with a first cut parallel to 1 (therefore 2) of the sides in 10 minutes, a second cut at right angles to the first cut can take anything from almost 0 to almost 10 minutes. The assumption is that the first cut bisects the square and so is halfway along a side. For a square which is s x s in size, you can vary the proportion between left and right sides from 0 to s, hence the infinite number of answers between 0 and 10 minutes!
Other topological shapes are of course possible such as an annular ring (donut). I’m not going to hurt my brain trying to cut a Möbius strip lengthwise!! 😂
This also assumes all cuts are made at right angles. If you make a 45 degree cuts then through the center it could take just over 14 minutes to make the single cut, and over 21 if you include the second "half" cut as well. If you cut near the corners it might only take a minute or two to make two cuts and end up with three pieces.
@@nurmr and that it is a “thin laminar” to preclude any 3 dimensional cuts!! If it is thick, you can put a cut through the plane of the shape - you could have two identical pieces… think of cutting through a cube or other shape with height breadth and depth. The question didn’t say you couldn’t think in 3 dimensions (conversely it didn’t say you could). There is no limit to our imagination!
You've ignored the grain issue. If you have only one saw, one of your cuts will be made across the grain with a ripsaw, or with the grain with a crosscut saw. That could make the second cut take longer than the first, if it's even possible at all!
@ I never was practical! Thanks for the wood specialist’s correction to a maths person’s rose tinted spectacles!
This is what happens when you know how to do something on paper, but never tried to do it in reality.
Illustration of the 3 most common math mistakes:
1. Missing minus sign
2. One off error
This is so obvious. I asked my 6th-grade students this, and the majority got it correct they got it right.
"Who hasn't made an off-by-one error in their life?"
I have. Then again, I'm not a teacher with access to the answer key.
Huh. I didn’t know this went so deep. At first, I thought about ratios and proportions.
Let's face it : Marie is not good at carpentry.
That explaination made so much more sense. The visual made it easier for me to understand.
It took Marie 5 minutes to find the saw, and another 5 minutes to make one cut to cut the board into two pieces. She now has the saw and another board of the same size as the first board. It will take 5 minutes for each of two cuts to make three equal size pieces. Therefore, the correct answer is 10 minutes.
But after making the cuts she has to put the saw away. This takes another 5 minutes because she has to decide where to place the saw so it will take 5 minutes to find it the next time she wants to use it. So, the teacher was right --- 15 minutes!
Requires making assumptions not stated in the problem. If we need to account for setup and cleanup time the answer is underdetermined because we don't actually know how long that takes; we have one equation with two unknowns
@@johnburgess2084 No, her husband had been using the saw and forgot to put it away, so she had to search for it. Normally, the saw hangs right here next to where she saws logs.
@@benroberts2222 As has been explained by many before me, there are as many correct answers as there are assumptions that can be made to fill in the missing data. Is the second piece of wood the same size and shape as the first? Did she just clip off the corners of the second piece of wood? Was she tired after cutting the first piece of wood? The missing data precludes one correct answer. Therefore, the assumptions I make make my answer correct for those assumptions.
Well, let me add that it never said into 2/3 equal sized pieces. We can assume the third piece can be a little corner piece that takes a minute. @@benroberts2222
This channel is one of the reasons why I love math.
This is probably one of the only times I have watched an educational video on my own and enjoyed it.
Oh this is funny. I had a cake problem in math class that I got “wrong” for the same logic by the teacher. The question was something like this. Joe has a cake that needs to feed 100 people, how many cuts does Joe need to make to get 100 pieces of cake. My answer was 18 cuts, 9 vertical and 9 horizontal. The teacher marked me wrong because 9x9 is 81 not 100. I challenged this and she insisted it was wrong. I asked the other kids in the class if they answered 18 and if so to raise their hand. About half raised their hands, then I asked them to put your hand down if you got it right. The only kids left were the ones the teacher didn’t like, including me. She didn’t hide the fact that she didn’t like us, and I challenged this with her again. She kicked me out of class, sent me to the office and I had even more fun there. Told the principal what had happened, I even had my test with me to show him. We went back to her class and she was dismissed while the principal fixed our papers. Found out a few of her favorite students got the wrong answers right even. We didn’t see her for 2 weeks. And I can’t say she treated me any better when she came back. The following school year I once again got her as a teacher and immediately had my schedule changed. When I took the sheet to her to sign she was surprised I didn’t want to be in her class again. I told her I didn’t feel like being beaten and abused again by her.
Her husband was the Principal of my high school the following year and up to my graduation and he was pretty cool. I actually liked him.
8:14 you could just do one extra cut from 5 cuts or 6 pieces for 6 cutsfor18 minutes because the question doesn’t say they all have to be vertical or horizontal
I was never good at these kind of problems during high school and now I kinda wish I had your video because it would’ve helped a lot
Why are we shocked anymore?
This has happened so much it should be shocking if a math teacher knows basic arithmetic.
Funnily enough once someone commented in one of your video saying that once teacher asked to solve this same question with different values and the teacher did the same mistake but when that person corrected the teacher, teacher's face was worth watching 😂😂😂😂
When I was trying to solve the answer through the thumbnail, I thought it said 20 minutes was wrong, so I went into the actual video and it turns out I was not wrong 😂
her answer is technically true if you cut it vertically.
no, it isn't because a "board" can be assumed to be significantly longer than it's wide. this would mean the time for the second, smaller cut is completely unknown. it would make the question unanswerable.
6:16 I’m sorry but disagree that we should give the teacher a break. While we all do make this mistake at least once, it’s while we are still learning about elementary math problems. An actual math teacher in a school should know better.
Actual teachers can make mistakes, it is how they react that matters. My teachers encouraged us to point out mistakes in the homework and/or test. I've had cases where a caught error became a free answer for the class. I've also had teachers who refused to either budge or elaborate on why they think they're right, so there are still casers where your point still stands, we just don't know which way the pendulum swings on this issue.
12 minute video talking about 1 mathematic question. Love it.
Problem is, while 1 cut creates 2 pieces, we are not told the dimensions of the second board, just that it is “another board”. So we are missing information. Assuming the second board is the same size as the first, it would be 10+10=20.
The assumption would be correct as there is no point in the question if it was lacking information.
Unless the board is in the shape of a pizza😅
If cutting a pizza into two pieces takes 10 seconds, how long would it take to cut a similar sized pizza into 3 pieces?
@@bornach15 seconds
@@johnluiten3686 Which means there may well be no point in the question.
@@RickyMaveety The dimensions may be assumed from the 2nd picture and the statement of “equal effort”. Now if the pictures are not to part of the puzzle, then perhaps. But I go upon what I see, not what I imagine.
2 pieces = 1 cut, 10 minutes per cut, so 2 cuts = 3 pieces = 20 minutes. How did the teacher bollix this up?
Well, because the teacher wasn't the sharpest tool in the shed.
Mary also needs to have her saw sharpened. . . 😅
Because the teacher took 10 minutes and divided by 2 to get 5, then multiplied by 3 to to get 15. Not realizing it is not the number of pieces but the number of cuts.
Man I remember in middle school where these questions were like 2 plus 2 for our tests
8:00 I would argue that they said 5 TO 11, they never said they watched all of season 11 just that they've gotten to it, in this case 6 is the right answer
I have to say on the last example the correct answer is 9 not 10 as the frog jumped out of the hole on the 9th day ,dosent fall back 2 feet and never even gets to day 10 11:58
Aha! You're off by one!
If the well is 12 feet deep, and the frog jump from 9 feet that day he only reach 12 feet which just exactly at the same height as the well which realistically resulting he can't jump out of the well, so the frog need a day more to jump off.
No, in day 9 the frog jumped to 11 feet and fall to 9 feet. So the frog need one more day to jump to 12 feet and get out of the hole
I like how it's all because the 'cut' and 'board' are two variables that can be taken into context totally differently from the preferred way.
4:25 - yeah creative, but not the same board and cut as the original question. Marie won't be able to cut half her post longways, but, if she did then the long cut would take much longer and the answer would be greater than 15mins (in fact it'd be greater than 20 mins)
But the problem never specified the shape of the board
I will admit, it fooled me at first. It seems to be intentionally designed as a fun trick question, an awnser that isn't the first thought.
Where simple maths meets DYI vids - brilliant. The essence is that the cuts take time, not the pieces
11:51 If you wanna be really pedantic, the answer is nine FULL days, then it escapes at the start of day 10.
No hes right
It takes the frog a full day to jump 3 feets