@@dflayneBecause you can't define the value of ❤ without knowing the value ⭐ since (❤=⭐+9). Simply writing 40 = (7+⭐)+❤ is the same, but a step back. Just replace ❤ with ⭐+9. I get that the question only asks what is ⭐+❤, but finding out each value seems to be realiable.
It’s not hard, but it is kind of a confusing way to format it and it took me a bit to figure out what the pattern was. Once I realized what it was, it was very easy
That happens to me all the time. The cashier looks at you and usually replies with something along the line of that’s too much money. Bill comes to 16.95 and you give them a 20 and a two dollar coin (I’m in Canada, we don’t have dollar bills, we have one and two dollar coins), instant deer in headlights look. Just give me back a 5 dollar bill and a nickel. I don’t think they actually know how to use the cash register, they just hit the Cash key like giving exact change and they can’t do the math in their head. Just enter $22.00 before you hit the Cash key and the machine will actually show you how much to give back.
I gave a teenage worker at an amusement park $20.75 for a $5.75 Icee. Me and the whole line stared at her doing mental math. I got my Icee and $25 back in change.
The way I did this was notice that the way the pyramid was built, if we call the 3 numbers on the bottom x, y, and z, the number shown at the top is (x + 2y + z). I could then use that to solve for star immediately. Once we know that, we can solve for heart by adding the 9, then add the two together. I got 33.
This was my method. I realised that the sum of 40 was obtained by adding the bottom left/right values once, but the middle number is added twice as you go up the triangle. Once you’ve worked out the bottom number the rest is trivial.
Nah, this is a nice age-appropriate puzzle for a 9 year old. Maybe not one that should be assigned as homework, but wouldn't be out of place in a childrens' puzzle book with matchstick puzzles and other logic excercises.
@@Pikachu132 Oh, I didn't mean it's too difficult when someone likes solving puzzles. Kids are usually amazing at such things. Under one condition - fun. That's a general school problem. It takes the fun out of learning. And we adults are masters in making really fun things into teadious tasks. I was lucky to have a dad, who understood the concept of problem solving and explaining things in simple terms. Many years later I found out it was a core of a Feymnan's technique for learning very complicated things - just try to put it in simple terms and use examples from everyday life. As any student, I suffered from a chronic lack of cash, so I tried to earn a bit by giving private tutoring in math and physics. I still remember one girl who was about to fail her classes in mid school. She hated both subjects. And after a month of tutoring, when she finally got her passing grades, she told me: "you know... Now I don't hate math and physics so much". The only thing I did was to explain those problems a bit differently, using examples she could relay to, showing the method of chopping a big and complicated problem into smaller and easier parts. Kids are great at problem solving. They just need adults to stay away from making that learning pitiful 😉
@@naginiriddle7091 Yes I agree, the base for solving this is a pattern recognition. But what you do after you recognize a pattern? You have to add and substract. You can do it with numbers, you can do it with fingers, you can do it with peas in a basket, you can draw kittens an dogs. You can name it whatever you want. But at the end you will have to take out some number of peas from one basket to find how many peas you have left - I think that's the core of substraction right there. It kind of reminds me a George Carlin's standup about euphemisms😏
@@ogi22 that isn't substitution though. That is subtraction, which any 9 year old HOPEFULLY has been taught how to do. Substitution requires variable equations where it is agreed a variable is to remain the same for all equations, and then to solve for the variable, you will substitute in another equation. That is algebra 2, for kids who are typically in high school. This doesn't require algebra to solve. Like I said, it is just pattern recognition, similar to sudoku. Yes, subtraction is involved, but you don't need anything other than that
My first instinct was "40 = blank box + heart" and "blank box = 7 + star" so ... "40 = 7 + star + heart" and then "33 = star + heart" which is the answer. Apparently this was the "clever" answer.
@@colors6692 right. The video waited until the end to cover the obvious path. I'm not sure if there's research suggesting that the other paths are more likely to be found in grade school math homework or something else. I didn't feel it was clever - often the videos actually do show at least one path I didn't think of, this one felt like it was stretching to fill time.
@CharlesBallowe How about "40 = blank box + ♡" Therefore ♡ = 40 and ☆ = 31. Isn't this logical too? There's no reason to assume that the blank box isn't really blank.
My logic was that 7 and 9 are two apart, and both 7 and 9 are being added to the same number to create the middle numbers and therefore the middle numbers must also be two apart, and the only way to do that to get 40 is 19+21 so the middle row is 19|21 and the rest of the puzzle solves itself from there.
I think I solved this is a pretty simple way: since we know that the middle number is the sum of the 2 numbers below it, I noticed that the top number would be the sum of of the outer numbers on the bottom row + 2 times the middle number. In reverse you just subtract the 2 outer numbers from the top (40-7-9) to get 24 which is 2*12. Thus the bottom middle number is 12 and can be used to calculate the remaining values
the biggest hurdle to understanding this problem is the blank section which can easily be misinterpreted as a 0 since there isn't even a place holder symbol to suggest that it has a value associated with it.
I did it like this: (star is x, heart is y) y = 9 + x 40 - y = 7 + x add the first equation to the second one: 40 = 16 + 2x 24 = 2x x = 12 then sostitute 12 to x: y = 9 + 12 y = 21 then the final answer is: x + y = 12 + 21 = 33
As others also noted, but I like to phrase it differently: All values come from the bottom and simply trickle up. However the middle value trickles up twice! So 40 is the sum of the bottom values, with the middle value added twice. This quickly gives you a middle value of 12.
The hardest part was figuring out what the question was actually asking me to do. At first I thought it was asking me to solve a ratio but then realized it's just a really badly written substitution problem. Math used to be straight forward and would just ask you to solve for X: 40 = (7+X) + (9+X). Now we have to decipher what the question is even asking us to do.
@peterwilson8039 When I was a kid we tested each skill with a matching question. We didn't pose a question on a skill as a guise for a test on a different skill.
@@MrGhosta5 It is reasonable to argue that a math class is also a logic and critical thinking class, therefore it is the same skill. Anyway, while I have encountered questions that have the issue you described, this problem actually says, at the top, what the exact question is. So your complaint is irrelevant.
I used a different method: I noticed immediately that the triangle is Pascal’s Triangle-so the top sum is equal to the bottom left plus the bottom right plus double the bottom center. That immediately solved the star to be 12. The heart is then 12+9. The Pascal’s Triangle method works even if additional rows were added to the bottom of the triangle.
I didn't know what Pascal's Triangle was until I read this comment, but this was the exact method I used while I was looking at the thumbnail. I wanted to know the relationship between the filled triangle's top number and bottom numbers, and applied the solution I found to the problem triangle to find the solution. I reverse engineered Pascal's Triangle without knowing.
star is x and heart is y for clarification. x+7+y is 40, or x+y is 33. x+9=y, so 33 is 2x+9; so 2x is 24, and therefore x is 12. now, 12+9 is 21. y=21. now, 40 is 2x+16, and we said 2x is 24, so 24+16 has to equal 40, which it does. i love being younger than everyone in my grade yet being better at math than almost all of them ❤️❤️❤️
I just used the fact that blank = 7 + star, to get to 7 + star + heart = 40. Meaning that star + heart = 33 I didn't bother working out the individual values at first but when I did I just used the 7 and the 9 to know that the heart and blank have a range of 2, meaning that they are 21 and 19 respectively. Then it's pretty simple to work out that the star is 12
@@maxhagenauer24 The 9 isn't completely pointless...just mostly. ;) While 7 + star + heart = 40 gives you star + heart = 33, without that 9 there you'd never be able to determine the individual values of star and heart.
@gswcooper7162 Yes but the question was the sum of star and heart, you could find it by finding each individual values, in which case you would need the 9, but you don't have to. That's what I mean by pointless, it's not needed.
@@maxhagenauer24 Me working out the individual values was just an extra bit that I did for fun, I thought that was fairly obvious to be honest. If you don't care about the individual values then just don't read my final paragraph lol
Another way to solve for 9 year olds who don't yet know algebra is to notice that in the middle of the pyramid the number on the left will always be 2 less than the number on the right since 9 is 2 greater than 7. Then you need to find two numbers which have a difference of 2 that add up to 40 which leads to 19 and 21. From these numbers you subtract 7 from the left and get 12 or 9 from the right and get 12. So star is 12 and heart is 21 and the sum is 33.
Star equals 12 and heart equals 21. It’s just algebra, consider star as x and heart as y and write out the equations (Star+7) + heart = 40 (star+9) = heart Therefore, (star+7) + (star+9) = 40 Meaning 2star + 16 = 40 and 2star = 24 Which means star equals 12 Since (star+9) = heart, (12+9) = heart and heart equals 21
It’s 33 and now realizing what the question is asking, it’s pretty obvious that I can just subtract 7 from 40. That said, I don’t know if that’s what the video did.
My initial approach was that the numbers in the middle row must be 2 apart (9 - 7). That means the blank must be 19 and the heart 21 in order to get 40. Then star is 12 and the solution is 33.
The fact that you don’t need to know star or heart individually actually makes this really easy. Blank (x) is 7 plus star, which then add to heart to make 40. So heart and star just have to make up the leftover after 7.
I imagine this is why the box was left blank instead of filled with its own shape - on an actual question paper it'd help to visualise this by drawing lines from the 7 and the star through that middle-left box up to the 40, along with one from the heart.
The way I did it was the 2 numbers that add to 40 must have a 2 digit difference (because of 7 and 9) therefor must be 19 and 21. The rest is pretty straight forward
My immediate thought was this is some simple simultaneous equations, which is not to say I would expect that of a 9 year old, but the baffled parents? I think so.
There is some ax^c+by^d+e where x increments on the horizontal axis and y increases on the vertical plane, but it isn’t clean cut in any fashion, and very unlikely would the solution be an integer if you were to find a,b,c,d,&e in this equation that works.
I saw the thumbnail, didn’t expect to solve it, then solved it without the video in 30 seconds, and thought I’d see why an adult was baffled by an arguably simple problem.
Each cell is the sum of the two below it. So 7 + x = y, 9 + x = z, y + z = 40. We only need to know x + z, so sub (1) into (3) for 7 + x + z = 40 and subtract 7 from both sides for x + z = 33. We don't even need to know what x or z are.
I solved it while only looking at the thumbnail, before I even clicked on the video. It took me about a minute to recognize the relationships between the numbers in the left triangle, and then about 10 seconds to come up with the last solution in the video.
This barely qualifies as algebra. It is more an exercise in recognizing the relevant unknown, and setting up the equation to solve for it. The heart is a red herring that looks important because the other 2nd row box is blank, but it is not. I think that is what is tripping people up.
@@mjbull5156 I was also talking more about the mentality. In my experience, those who gloat over the fact they "never used algebra" also refuses to do any form of equations through pattern recognition. One example I use is that a parent buying sheet cake for their children's party. To make sure you have enough, you need to make sure the number of available pieces at least match twice the number of attendees (as you should assure 2 pieces per person). This can be expressed in an algebraic formula of X=2y/z. However this algebra often occurs without the person even thinking about it. If I recall my psychology, this would translate into them only seeking pattern recognition with their delta brainwaves (surface memory recall) instead of their beta brainwaves (focus), which is the same reason people get caught by simple logical problems like how to spell simple words.
i took what seemed to be the most straightforward approach. first thing i thought of was to add the two bottom numbers and subtract that from the top number then divide that by 2 to get the star. then all i had to do was add the star to the bottom right. there are a lot of different solutions to this as you said. my thinking was that since i noticed the same number was added twice, and no other arithmetic operators asides from addition seemed to be used, i could ignore the middle row entirely. and since i already knew the pattern i just followed it to get the heart and the blank space.
The total is 40. This means that you need to figure out what number can be added to 7 and 9 to make two numbers that equal 40. 7+12= 19 9+12=21 19+21=40 And this is based on the rules established at the start before his explanation.
Solved on the thumbnail before I clicked for the solution. Pretty easy if you make an algebraic equation but also not too hard to solve if you’re looking for patterns. I like it!
My brain definitely defaulted to copying the pattern method simply because it didn't want to think about the math and hoped to solve the problem through recognition.
If you were really stuck, you could start with star = 1, which is too low, and increase star until star = 12 solves the triangle. What I've noticed when helping people with maths is how reluctant students are just to try things to see what happens. Also, doing this basic process reveals how the triangle works - every time you add 1 to star, you add 2 to the apex. Then, you can work out for yourself that 40 = (7+star) + (star + 9) - even if you didn't see that immediately.
37 secs ago ?? This is literally the earliest i have ever been on any video Edit : I used the 1st way but in the reverse manner so that I get 21 and 19 faster ... I started with 25, 15 and then found out that ♡ = 21 and ☆ = 12 ... thus 12 + 21 = 33
This popped up in my recommended for some reason. I was trying to solve it from the thumbnail, so I didn’t know the rule you opened the video with. Because of this, my first step was trying to find out the rule. After that, I immediately went for the algebra solution.
The puzzle is solvable with basic algebra, but the parent might have assumed the teacher wouldn't possibly throw an algebra problem at a third-grader, and was looking for something even simpler.
@@AndRooooooo If you realise there are rules to it, which somebody who hasn't been dealing with this in years well might not. Overall it's a case of poor presentation. The problem itself is pretty trivial.
Immediately went to solving algebraically through a system of equations. Once I figured it out, I thought "Well..... they teach 9 years olds algebra now, I guess."
Someone see my solution: What i did was kept the blank space and heart as 20 and 20 respectively. Now ,star is common in both 7+☆=blank and 9+☆=♡. Therefore the difference between the blank and heart should be 2 as 9-7=2. So i subtracted 1 from 20 and adde 1 to 20 to get the values of ♡=21 and blank=19. Then i got ☆=12. Therefore,☆+♡=21+12=33. Simple!!!!!!!!!
My solution was close to yours. I reasoned that the average of the sum of blank plus heart was 20. So subtracting 7 and 9 from 20 yields 13 and 11 respectively. The midpoint of 11 and 13 is 12 so that is the value for star. Adding 12 to the values on the bottom row solves the puzzle
The correlation between numbers in a 3 level pyramid based on the given rule is very interesting indeed. Actually we don't even need to find out values of ♥ & ✳ The relation can be defined as Apex - a base corner = Sum of diagonal pair touching the other side 40 - 7 = ♥ + ✳ = 33 13 - 2 = 7 + 4 = 11 13 - 3 = 6 + 4 = 10 40 - 9 = ✳ + void = 31
This is remarkably easy. Just like any algebra problem, you identify what information you are given and find overlaps you can use to solve the problem.
@@engi_games The blank space is clearly (7 + star). Therefore ((7 + star) + heart) = 40. Subtract 7 from both sides, star + heart = 33. How is that not how algebra works?
It's not terribly difficult to just solve for all three variables, Heart, Star and Blank, using substitution: H = 9 + S B = 7 + S B + H = 40 --- (7 + S) + (9 + S) = 40 2S + 16 = 40 2S = 24 S = 12 --- H = 9 + 12 H = 21 B = 7 + 12 B = 19 --- 21 + 19 = 40 Star = 12, Heart = 21, Blank = 19 That seems more useful to me...
@tariqoner4678 I regret to inform you that what you have replied is, indeed, 2 equations. I would still consider this problem easy for a 9yo, it's just so simple.
@@ImpKraken dude, what kind of Xavier school for gifted children did you go to? The average 9 year old is still trying to wrap their head around fractions and decimals being the same thing. The word 'equation' has probably never even been said to them.
Interesting, I don't recall ever doing these. Took me awhile to figure out the rules pausing at the start. My approach went back to my old-school engineering days: 2 unknowns -> Create 2 equations. I did 7 + 2 * star + 9 = 40 and 9 + star = heart. Use the first equation to get star = 12, second equation to get heart = 21.
Do not be discouraged by something that seems impossible. In the first triangle you can figure out a rule: base corner plus star plus heart equals top. Works with the mirror combination too. Change the numbers in the base, and you'll notice that the rule stands. Then apply it to the puzzle. Don't be a stuck-up mathematician. Open your mind. Then, if you care, formalize your findings. But I think the main purpose of the quiz was to train young minds into being open, into becoming nimble. It's not too late for parents to take advantage.
This is a problem that should not be given to kids. All it will do is result in frustration, turn them off to math, and is really just a waste of time.
Found an alternative method that a 9-year old could use as well: We can assume that the corners (7 & 9) are still a part of the top, (40) so we could simplify by combining the bottom corners into (16) and subtract it from (40) that will leave us with the value (24) to be used as various possibilities for Star. We could brute force it and count down rather than count up, but we could also test by distributing the value equally across the Blank and Heart, halving the value for (12) for the same conclusion of [33]
A quick adjustment when using the guess and check method: After your first guess, the remainder of the total of the middle values subtracted from the top value, divided by 2 is the amount needed to add (or subtract) from the bottom number. Your example = (40 - 18) / 2 = 11 , so 11 + 1 = 12
@@stigmontgomery7901 oh I always appreciate the “here’s three ways” as sometimes seeing a different solution approach helps for a completely different problem, or just understanding how people can see the world differently. But as commented elsewhere the top number is left + 2*middle + right of the bottom row. In this case I’m not sure other approaches added much insight.
An easier way to think about it is that the top number is always the sum of the bottom row, counting the middle number twice. So 7 + 2x(star) + 9 = 40 so (star) = 12.
Achieved solution 42 seconds into the video. I understood the first pyramid before you explained the rule, which made the second pyramid easy. Subtract the two numbers at the bottom from the top. Divide the difference by 2. The remainder is star. Add remainder to the number under heart, and the sum is heart. Add remainder and number under blank to fill blank. Add blank and heart to prove.
I did it the last way, but forgot that i was just looking for the sum of star and heart, not the individual values of star and heart, so i proceeded to solve them as well.
Pausing at 0, I think I solved it without any extra instruction. Star is 12, and heart is 21. Answer is 33. If correct, I based it off of the first triangle, where 13 can only be added up to by using a corner piece, the middle piece, and the opposite side piece of the corner piece to get the top piece's sum. So 2+4 is 6, +7 is 13. And 3, 4, 6 is also 13 from the opposite side. The middle sections are found by adding the left corner and middle bottom together to get the left middle piece, and same deal with the right side. So now the star and heart. Work backwards. 40 - 7 is 33 (irony?) 40 - 9 is 31. So we need 3 numbers that fulfill the missing parts of that missing sum. Since we know that the corner pieces must be started with, and the middle rank is (seemingly) always high in number than the bottom rank, then the bottom rank can't have a very high number in the middle. But which side to start with? Since we are missing all the 'middle pieces' so to speak, we start with the left side. Why? Because all we have to do is ask ourselves, "what number allows us to split the 33 up so that the bottom number is still going to be lower than the middle rank numbers?" Well, it can't be 8, because that would be lower than both the corner numbers, and the middle bottom of the left triangle is larger than the corner numbers. So it probably needs to be larger too. So it can't be less than 10. But how to find out if it's the right number? Easy. Add the 7 to 10, to get 17, then add 19 (9 +10). If you get 40 (you won't), you got the right number. It was not the right number, the result is 36. So we're missing 4 digits somewhere in that chain. Okay, let's add 2 then, because 1 probably won't be enough. So now it's 7 + 12 = 19, and 9+12=21. Sum is 40. Okay, so we have the star, and the empty space filled. So now the heart. Well, 9+12=21, so heart must be 21. 12+21=33 This might not be the 'right' way to do it, but I got the right answer, right? This took me, maybe 3 minutes to solve.
Another approach could be that the numbers on the middle row are going to be always with a difference of 2. Then we can ask what two numbers, with a difference of 2 between them, add up to 40? Divide 40 by two, and add and subtract 1 to each side. The answer gives you "heart" and "blank". Having those, you can easily get "star". But I liked your third approach more.
For simplicity of explanation, let's call the star x, the heart y, and the blank space z. So, z=7+x, y=9+x, and 40=y+z, which can also be written 40=(7+x)+(9+x), which simplifies to 40=16+2x, which we can solve to 24=2x and then to 12=x. Now that we know x is 12, we can find that y is 21 (12+9) and z is 19 (7+12), and thus x+y (or star+heart) equals 33. I don't even teach math, I'm an English Language teacher.
We can use this approach, we'll take the top number (40 in this case as an anchor). Third rows 1st+2nd+2nd+3rd element sum should be equal to 40 as in the third row middle element is getting overlapped once. So we can say 2nd element= (40-7-9)/2 = 12 now heart= (9+12)=21. Heart+star=33
My first instinct was to notice that the number on top is the sum of the middle level, and the ones in the middle are the sum of the bottom level with the middle number twice. So 40 = 7+2x+9 40-16=24 24/2=12. Star is 12 and we can just work upward from there. 9+12 is 21, and 7+12 is 19. 21+19=40.
I could not think of a way for a 9 yo to solve this problem. No algebra for sure. Went through the entire video. Very very interesting to see how they could solve!
An alternative approach is to think how to sum up to 40. The equal share would be 20+20, but this would require the two bottom corners to be equal. They have a distance of two and this distance needs to be kept in the middle row, because both will get added the exact same number (the middle bottom field). Creating the gap of two leads to 19 + 21, so we already have heart. And from there getting star is easy.
I was looking at the thumbnail and kind of quickly realized that 2 and 4 are below 6, and 4 and 3 are below 7. Once I got the pattern from that it was simple. I added 7 and 9 to get 16, then added 24 to get 40. and since the number at the top will be the bottom left, bottom right, and bottom middle (times 2) I could solve for star as 12. (or half of 24). after confirming what I had deduced, I then solved for heart being 21 (12+9) and from there, star + heart = 33 I'm pretty happy with myself for solving this.
0:56 Reckon ♥+⭐=33. First lets get rid of the Emoji for the sake of my sanity and get some PROPER variables in there. If we label the pyramid top to bottom: ♥=C ⭐=E [A] [B][C] [D][E][F] These are the rules of the Pyramid. [A] A=B+C [B][C] B=D+E C=E+F [D][E][F] We can rewrite this into an equation.(Mind you I'm not completely sure of the right way to notate this...) [B] [C] (D+E)+(E+F)=A Now let's enter the variables we know. D=7, F=9, A=40 [B] [C] (7+E)+(E+9)=40 My first impulse is to combined like terms. E2+16=40 Then we can cancel out the 16 by subtracting it from 40. E2=24 Then we can cancel out the two by dividing by two. E=12 And we can plug that into the original to check our work, [B] [C] (7+12)+(12+9)=40 [B] [C] 19+21=40 and it does. So we can plug all that into the Pyramid. [40] A=19+21 [19][21] B=7+12 C=12+9 [7][12][9] C+E= 21+12=33
Legit thought this was gonna be a compilation of questions that adults struggled with instead of just the one in the thumbnail. I solved this in well under half the time and I was terrible at maths as a kid. The method you used overcomplicated a very simple question.
7 and 9 are separated by 2. Therefore the resulting numbers in the middle row, being the sums of each number, added independently to star will be separated by 2. I divided 40 down the middle and removed a 1 from column 'a' and added it to column 'b'. I then subtracted the corresponding numbers from the bottom row to solve for star.
any arbitrary sequence of numbers can have observable patterns, but that doesn't mean you can continue the sequence based on the observed pattern unless the rules of the pattern are specified as part of the problem. many such cases
Personally I found that the number in the bottom middle is used twice to make the number at the top, and the outside numbers used once. So I subtract 7 and 9 from 40 to get to 24, then divide that by 2 and then have 12 in the bottom middle. From there we can work out the 2 numbers above it by simple addition. getting 19 and 21. We can check that 19 and 21 add up to 40, so we know all numbers are correct. Then we can add 12 and 21 for the answer of 33.
It’s kind of easy. Just takes a second to work out the mechanics. Each layer feed into next. Total for each row will end up being Lt + 2*Mid + Rt from bottom row, since Mid gets added into both Right and Left in second row. So 40 = 7 + 2*mid + 9 Mid = 12 = Star Heart = 9+ Star = 21 Star + heart = 33
The only difficulty is to figure out that the absence of symbol in the left of the second raw isn't equivalent to 0. As soon as you name it x, there no longer any difficulty. Most of this riddles build upon intentional wrong formalization.
*Alternative approach*
The whole pyramid can be written simply as:
40 = (7 + ★) + (★ + 9)
And then you take it from there.
That's how I saw (and solved) it.
33
I took the approach the LHS is 2 less than the RHS : the heart is 21. Given the heart is star + 9, the star is 12. Heart + star is 33.
why are you making this so difficult? It is far easier just to write 40 = (7 + star) + heart. You can go straight to that one, simple equation.
@@dflayneBecause you can't define the value of ❤ without knowing the value ⭐ since (❤=⭐+9). Simply writing 40 = (7+⭐)+❤ is the same, but a step back. Just replace ❤ with ⭐+9.
I get that the question only asks what is ⭐+❤, but finding out each value seems to be realiable.
It's not a particularly difficult problem, but I definitely didn't expect to see it being given at such a young age.
It’s not hard, but it is kind of a confusing way to format it and it took me a bit to figure out what the pattern was. Once I realized what it was, it was very easy
@@oxedward4738 no, u're not 9 yrs old
Eh, I solved these kinds of problems easily for fun at 7
@@oxedward4738it took me one minute, eh
@@Blue96YT ok
To be fair, most adults are baffled by splitting a restaurant bill.
Lmao 😂
Women.. 🍵
Haha so true
2☆ = 40 - 9 - 7
This is easier than splitting most restaurant bills! 😂
@@mickdavies5647 yeah but coming up with the idea of the 2⭐is the hard part for these adults.
At a coffee shop my bill was $5.25.
I gave the barista a $10 bill and a quarter.
It was like watching the Hindenburg 2.0
Uhh they don't want the coins either 😂 maybe they were hoping to give you a bunch of change that other people keep giving them 😂
That happens to me all the time. The cashier looks at you and usually replies with something along the line of that’s too much money. Bill comes to 16.95 and you give them a 20 and a two dollar coin (I’m in Canada, we don’t have dollar bills, we have one and two dollar coins), instant deer in headlights look. Just give me back a 5 dollar bill and a nickel. I don’t think they actually know how to use the cash register, they just hit the Cash key like giving exact change and they can’t do the math in their head. Just enter $22.00 before you hit the Cash key and the machine will actually show you how much to give back.
the barista didn't know how much the tip was and his/her brain shortcircuited
I gave a teenage worker at an amusement park $20.75 for a $5.75 Icee. Me and the whole line stared at her doing mental math. I got my Icee and $25 back in change.
@@joepiazza3756 Sorry, I've got to say it: that's not okay. Maybe help someone instead of taking advantage of them.
The way I did this was notice that the way the pyramid was built, if we call the 3 numbers on the bottom x, y, and z, the number shown at the top is (x + 2y + z). I could then use that to solve for star immediately. Once we know that, we can solve for heart by adding the 9, then add the two together. I got 33.
This was my method. I realised that the sum of 40 was obtained by adding the bottom left/right values once, but the middle number is added twice as you go up the triangle. Once you’ve worked out the bottom number the rest is trivial.
This was my approach as well.
Same instinct here
Me too
Same here :)
To be fair, that REALLY is a difficult problem for a 9yo. It requires figuring out a way to solve a problem by substitution.
Nah, this is a nice age-appropriate puzzle for a 9 year old. Maybe not one that should be assigned as homework, but wouldn't be out of place in a childrens' puzzle book with matchstick puzzles and other logic excercises.
@@Pikachu132 Oh, I didn't mean it's too difficult when someone likes solving puzzles. Kids are usually amazing at such things. Under one condition - fun. That's a general school problem. It takes the fun out of learning. And we adults are masters in making really fun things into teadious tasks.
I was lucky to have a dad, who understood the concept of problem solving and explaining things in simple terms. Many years later I found out it was a core of a Feymnan's technique for learning very complicated things - just try to put it in simple terms and use examples from everyday life. As any student, I suffered from a chronic lack of cash, so I tried to earn a bit by giving private tutoring in math and physics. I still remember one girl who was about to fail her classes in mid school. She hated both subjects. And after a month of tutoring, when she finally got her passing grades, she told me: "you know... Now I don't hate math and physics so much". The only thing I did was to explain those problems a bit differently, using examples she could relay to, showing the method of chopping a big and complicated problem into smaller and easier parts. Kids are great at problem solving. They just need adults to stay away from making that learning pitiful 😉
Substitution is not required. It is just pattern recognition. If a 9 year old can do sudoku, they can solve this no problem
@@naginiriddle7091 Yes I agree, the base for solving this is a pattern recognition. But what you do after you recognize a pattern? You have to add and substract. You can do it with numbers, you can do it with fingers, you can do it with peas in a basket, you can draw kittens an dogs. You can name it whatever you want. But at the end you will have to take out some number of peas from one basket to find how many peas you have left - I think that's the core of substraction right there.
It kind of reminds me a George Carlin's standup about euphemisms😏
@@ogi22 that isn't substitution though. That is subtraction, which any 9 year old HOPEFULLY has been taught how to do.
Substitution requires variable equations where it is agreed a variable is to remain the same for all equations, and then to solve for the variable, you will substitute in another equation. That is algebra 2, for kids who are typically in high school.
This doesn't require algebra to solve. Like I said, it is just pattern recognition, similar to sudoku. Yes, subtraction is involved, but you don't need anything other than that
My first instinct was "40 = blank box + heart" and "blank box = 7 + star" so ... "40 = 7 + star + heart" and then "33 = star + heart" which is the answer. Apparently this was the "clever" answer.
Yeah I did the same thing
Everyone did it that way bro...nothing clever about that solution🤣🤣
@@colors6692 right. The video waited until the end to cover the obvious path. I'm not sure if there's research suggesting that the other paths are more likely to be found in grade school math homework or something else. I didn't feel it was clever - often the videos actually do show at least one path I didn't think of, this one felt like it was stretching to fill time.
@@colors6692yeah he put clever in quotation to show he doesnt think thay but thats what they said
@CharlesBallowe How about "40 = blank box + ♡"
Therefore ♡ = 40 and ☆ = 31.
Isn't this logical too? There's no reason to assume that the blank box isn't really blank.
As my old maths teacher said: "A lot of things are just quadratic equations in disguise."
My logic was that 7 and 9 are two apart, and both 7 and 9 are being added to the same number to create the middle numbers and therefore the middle numbers must also be two apart, and the only way to do that to get 40 is 19+21 so the middle row is 19|21 and the rest of the puzzle solves itself from there.
Same, but I am way worse at explaining my thought process.
Ywp this is simple way, no algebra required
True. Only sum, and subtraction are needed.
That’s how I did it.
This is also how I achieved 33.
I think I solved this is a pretty simple way: since we know that the middle number is the sum of the 2 numbers below it, I noticed that the top number would be the sum of of the outer numbers on the bottom row + 2 times the middle number. In reverse you just subtract the 2 outer numbers from the top (40-7-9) to get 24 which is 2*12. Thus the bottom middle number is 12 and can be used to calculate the remaining values
Simply 40-7-9= 2 x star. So star= 12 . Rest follows.
This was also my first idea...
yeah, but what is 12+9?
not so easy anymore, hm?
@@spitalhelles338021, and 7+12 is 19 and 19 + 21 = 40
@@spitalhelles3380holy that’s hard
@@spitalhelles3380 129, ez!
the biggest hurdle to understanding this problem is the blank section which can easily be misinterpreted as a 0 since there isn't even a place holder symbol to suggest that it has a value associated with it.
Easiest MYD problem by far
don't take this w from me
I agree, got it straight away 😮
True, I did it in my mind easily
Good for us or more particularly, me! I’d like such an easy MYD problem more often than… hm, how many years has it been?😅
@andrewhooper7603 It's all good. We have to take the W's where we can get them.😂😂
Feels good to be able to solve a homework puzzle.
this one is quite easy ngl
It's for 9 year olds
@@NabeelFarooqui lmao
true, solved it in around 30 secs
Solved it in my head before clicking on the video
@@wasikancb same
I did it like this:
(star is x, heart is y)
y = 9 + x
40 - y = 7 + x
add the first equation to the second one:
40 = 16 + 2x
24 = 2x
x = 12
then sostitute 12 to x:
y = 9 + 12
y = 21
then the final answer is:
x + y = 12 + 21 = 33
As others also noted, but I like to phrase it differently:
All values come from the bottom and simply trickle up. However the middle value trickles up twice!
So 40 is the sum of the bottom values, with the middle value added twice. This quickly gives you a middle value of 12.
That is how I solved it as well. And then once you have that, finding
The hardest part was figuring out what the question was actually asking me to do.
At first I thought it was asking me to solve a ratio but then realized it's just a really badly written substitution problem.
Math used to be straight forward and would just ask you to solve for X: 40 = (7+X) + (9+X). Now we have to decipher what the question is even asking us to do.
Sometimes the point of a test question is to see if the student is smart enough to understand the instructions. 😊
@peterwilson8039 When I was a kid we tested each skill with a matching question. We didn't pose a question on a skill as a guise for a test on a different skill.
@@MrGhosta5 It is reasonable to argue that a math class is also a logic and critical thinking class, therefore it is the same skill.
Anyway, while I have encountered questions that have the issue you described, this problem actually says, at the top, what the exact question is. So your complaint is irrelevant.
Just like real life
I used a different method: I noticed immediately that the triangle is Pascal’s Triangle-so the top sum is equal to the bottom left plus the bottom right plus double the bottom center. That immediately solved the star to be 12. The heart is then 12+9.
The Pascal’s Triangle method works even if additional rows were added to the bottom of the triangle.
Next you'll be telling me the numbers in the triangle can also be used as the coefficients of polynomial equations.
I would be impressed, if he hadn't told you that at the start of the video.
I didn't know what Pascal's Triangle was until I read this comment, but this was the exact method I used while I was looking at the thumbnail. I wanted to know the relationship between the filled triangle's top number and bottom numbers, and applied the solution I found to the problem triangle to find the solution.
I reverse engineered Pascal's Triangle without knowing.
star is x and heart is y for clarification.
x+7+y is 40, or x+y is 33.
x+9=y, so 33 is 2x+9; so 2x is 24, and therefore x is 12.
now, 12+9 is 21. y=21. now, 40 is 2x+16, and we said 2x is 24, so 24+16 has to equal 40, which it does.
i love being younger than everyone in my grade yet being better at math than almost all of them ❤️❤️❤️
this is the way i did it /srs.
I just used the fact that blank = 7 + star, to get to 7 + star + heart = 40.
Meaning that star + heart = 33
I didn't bother working out the individual values at first but when I did I just used the 7 and the 9 to know that the heart and blank have a range of 2, meaning that they are 21 and 19 respectively. Then it's pretty simple to work out that the star is 12
@TravisGn02 Even easier, you don't need to know the 9 at all, it is pointless in this problem because you only need to look at the others.
The kind of problem that leaves you wondering if there's anything more to it?
@@maxhagenauer24 The 9 isn't completely pointless...just mostly. ;) While 7 + star + heart = 40 gives you star + heart = 33, without that 9 there you'd never be able to determine the individual values of star and heart.
@gswcooper7162 Yes but the question was the sum of star and heart, you could find it by finding each individual values, in which case you would need the 9, but you don't have to. That's what I mean by pointless, it's not needed.
@@maxhagenauer24 Me working out the individual values was just an extra bit that I did for fun, I thought that was fairly obvious to be honest. If you don't care about the individual values then just don't read my final paragraph lol
Once you realize that each box is the sum of the two boxes below it it's not too tough, but expecting a 9-year old to solve it is kinda nuts.
Another way to solve for 9 year olds who don't yet know algebra is to notice that in the middle of the pyramid the number on the left will always be 2 less than the number on the right since 9 is 2 greater than 7. Then you need to find two numbers which have a difference of 2 that add up to 40 which leads to 19 and 21. From these numbers you subtract 7 from the left and get 12 or 9 from the right and get 12. So star is 12 and heart is 21 and the sum is 33.
That's exactly my solution.
Star equals 12 and heart equals 21.
It’s just algebra, consider star as x and heart as y and write out the equations
(Star+7) + heart = 40
(star+9) = heart
Therefore,
(star+7) + (star+9) = 40
Meaning
2star + 16 = 40 and 2star = 24
Which means star equals 12
Since (star+9) = heart, (12+9) = heart and heart equals 21
Brooooooooo, I would’ve got this wrong because I answered the values of star and heart and didn’t answer what them added together equaled…. Bruh
It’s 33 and now realizing what the question is asking, it’s pretty obvious that I can just subtract 7 from 40. That said, I don’t know if that’s what the video did.
My initial approach was that the numbers in the middle row must be 2 apart (9 - 7). That means the blank must be 19 and the heart 21 in order to get 40. Then star is 12 and the solution is 33.
I can't answer any of his puzzles correctly, but this one was child's play.
The fact that you don’t need to know star or heart individually actually makes this really easy. Blank (x) is 7 plus star, which then add to heart to make 40. So heart and star just have to make up the leftover after 7.
I imagine this is why the box was left blank instead of filled with its own shape - on an actual question paper it'd help to visualise this by drawing lines from the 7 and the star through that middle-left box up to the 40, along with one from the heart.
The way I did it was the 2 numbers that add to 40 must have a 2 digit difference (because of 7 and 9) therefor must be 19 and 21. The rest is pretty straight forward
My immediate thought was this is some simple simultaneous equations, which is not to say I would expect that of a 9 year old, but the baffled parents? I think so.
There is some ax^c+by^d+e where x increments on the horizontal axis and y increases on the vertical plane, but it isn’t clean cut in any fashion, and very unlikely would the solution be an integer if you were to find a,b,c,d,&e in this equation that works.
I saw the thumbnail, didn’t expect to solve it, then solved it without the video in 30 seconds, and thought I’d see why an adult was baffled by an arguably simple problem.
Each cell is the sum of the two below it. So 7 + x = y, 9 + x = z, y + z = 40. We only need to know x + z, so sub (1) into (3) for 7 + x + z = 40 and subtract 7 from both sides for x + z = 33. We don't even need to know what x or z are.
I solved it while only looking at the thumbnail, before I even clicked on the video. It took me about a minute to recognize the relationships between the numbers in the left triangle, and then about 10 seconds to come up with the last solution in the video.
Adult: I never used algebra in real life!
Kids: it shows.
This barely qualifies as algebra. It is more an exercise in recognizing the relevant unknown, and setting up the equation to solve for it. The heart is a red herring that looks important because the other 2nd row box is blank, but it is not. I think that is what is tripping people up.
@@mjbull5156 I was also talking more about the mentality. In my experience, those who gloat over the fact they "never used algebra" also refuses to do any form of equations through pattern recognition.
One example I use is that a parent buying sheet cake for their children's party. To make sure you have enough, you need to make sure the number of available pieces at least match twice the number of attendees (as you should assure 2 pieces per person). This can be expressed in an algebraic formula of X=2y/z. However this algebra often occurs without the person even thinking about it.
If I recall my psychology, this would translate into them only seeking pattern recognition with their delta brainwaves (surface memory recall) instead of their beta brainwaves (focus), which is the same reason people get caught by simple logical problems like how to spell simple words.
This channel is reviving my love for math.
Heart is 21, star is 12
That's what I said.
i took what seemed to be the most straightforward approach. first thing i thought of was to add the two bottom numbers and subtract that from the top number then divide that by 2 to get the star. then all i had to do was add the star to the bottom right. there are a lot of different solutions to this as you said.
my thinking was that since i noticed the same number was added twice, and no other arithmetic operators asides from addition seemed to be used, i could ignore the middle row entirely. and since i already knew the pattern i just followed it to get the heart and the blank space.
The total is 40. This means that you need to figure out what number can be added to 7 and 9 to make two numbers that equal 40.
7+12= 19
9+12=21
19+21=40
And this is based on the rules established at the start before his explanation.
Solved on the thumbnail before I clicked for the solution. Pretty easy if you make an algebraic equation but also not too hard to solve if you’re looking for patterns. I like it!
Easy enough to do so in your head. Just a small system of equations
My brain definitely defaulted to copying the pattern method simply because it didn't want to think about the math and hoped to solve the problem through recognition.
this video did not need to be 8 minutes long
I often wish we could speed videos up more than 2x.
This guy wasted time doing the “throw random numbers to see what works” method.
There's an extension for computer browsers called "Enhancer for RUclips" which allows you to speed up videos past 2x speed, among other features.
Yeah
If you were really stuck, you could start with star = 1, which is too low, and increase star until star = 12 solves the triangle. What I've noticed when helping people with maths is how reluctant students are just to try things to see what happens. Also, doing this basic process reveals how the triangle works - every time you add 1 to star, you add 2 to the apex. Then, you can work out for yourself that 40 = (7+star) + (star + 9) - even if you didn't see that immediately.
37 secs ago ??
This is literally the earliest i have ever been on any video
Edit : I used the 1st way but in the reverse manner so that I get 21 and 19 faster ... I started with 25, 15 and then found out that ♡ = 21 and ☆ = 12 ... thus 12 + 21 = 33
Same
This popped up in my recommended for some reason. I was trying to solve it from the thumbnail, so I didn’t know the rule you opened the video with. Because of this, my first step was trying to find out the rule. After that, I immediately went for the algebra solution.
That was pretty simple honestly, 40-(7+9)=24, so we get 7+12+12+9 = 19+21 = 40
So we get 21+12 = *33*
That's how I did it too. Nice to be able to do one of these in my head.
Three equations three unknowns. This should not baffle adults.
Star = 12
Heart = 21
Edit: Sum = 33
It’s impressive for nine year olds that’s for sure. It was easy to solve using algebra that kids that age wouldn’t have access to yet
In about 7 seconds from the thumbnail. I'm trying to figure out what was supposed to be so baffling about this.
Possibly if the pyramid rules weren't explained in the problem?
@@michaelsorensen7567The "rules" are obvious by examining the completed triangle though..
The puzzle is solvable with basic algebra, but the parent might have assumed the teacher wouldn't possibly throw an algebra problem at a third-grader, and was looking for something even simpler.
@@AndRooooooo If you realise there are rules to it, which somebody who hasn't been dealing with this in years well might not. Overall it's a case of poor presentation. The problem itself is pretty trivial.
The nine year old: when am I going to use this in real life?
Parent:
I figured it out by realizing the bottom row was essentially: 7+star+star+9=40. And that means 40-(7+9) = 2x star.
Wow. The only time I could solve one of these before clicking the video - just from the thumbnail.
(7+S)+(S+9)=40
2S+16=40
2S=24
Star=12
Heart=9+12
Heart=21
H+s=33 indeed
Immediately went to solving algebraically through a system of equations. Once I figured it out, I thought "Well..... they teach 9 years olds algebra now, I guess."
Someone see my solution:
What i did was kept the blank space and heart as 20 and 20 respectively. Now ,star is common in both 7+☆=blank and 9+☆=♡. Therefore the difference between the blank and heart should be 2 as 9-7=2. So i subtracted 1 from 20 and adde 1 to 20 to get the values of ♡=21 and blank=19. Then i got ☆=12. Therefore,☆+♡=21+12=33.
Simple!!!!!!!!!
My way of thinking without "complex" calculations
My solution was close to yours. I reasoned that the average of the sum of blank plus heart was 20. So subtracting 7 and 9 from 20 yields 13 and 11 respectively. The midpoint of 11 and 13 is 12 so that is the value for star. Adding 12 to the values on the bottom row solves the puzzle
The correlation between numbers in a 3 level pyramid based on the given rule is very interesting indeed.
Actually we don't even need to find out values of ♥ & ✳
The relation can be defined as
Apex - a base corner = Sum of diagonal pair touching the other side
40 - 7 = ♥ + ✳ = 33
13 - 2 = 7 + 4 = 11
13 - 3 = 6 + 4 = 10
40 - 9 = ✳ + void = 31
(7+✡)+❤ = 40
✡+❤ = 40 - 7 = 33
exactly. The 9 is completely irrelevant to the problem.
@@otakurocklee
7+✡+9+✡=40
✡=12
9+✡=21=❤
❤+✡=33
Wrong ⭐
@@AndrewBlucher Is this getting political. If it's going to be a maths war, I'm backing the ✡.
@@craigsaunders7037 Math is not political, it's factual.
The mid-left box is as vacant as the person's brain who made up this problem.
star is just (40-7-9)/2 = 12
heart is then 9+12=21
so 33
This is remarkably easy. Just like any algebra problem, you identify what information you are given and find overlaps you can use to solve the problem.
Huh? Why such a long video for such a simple problem? 7 + star + heart = 40. star + heart = 33. The 9 plays no role.
I like your solution, but. Clean.
That’s, not how algebra works
@@engi_games What? He’s doing a RUclips comment, not algebra. Understanding basic algebra is only one requirement for understanding the comment.
@@engi_games The blank space is clearly (7 + star). Therefore ((7 + star) + heart) = 40. Subtract 7 from both sides, star + heart = 33. How is that not how algebra works?
Just saying star + heart = 33 is not the final solution. You still need the 9 to solve for them individually.
Star is 12, heart is 21. Easy. Better group question than a single one, teach the kids to appreciate the smart one in the bunch.
40=blank+heart
blank=7+star
Therefore:
7+star+heart=40
Subtract 7 from both sides
Star + heart = 33
Easy 😂
It's not terribly difficult to just solve for all three variables, Heart, Star and Blank, using substitution:
H = 9 + S
B = 7 + S
B + H = 40
---
(7 + S) + (9 + S) = 40
2S + 16 = 40
2S = 24
S = 12
---
H = 9 + 12
H = 21
B = 7 + 12
B = 19
---
21 + 19 = 40
Star = 12, Heart = 21, Blank = 19
That seems more useful to me...
If a 9 year old was given this math problem, they would be exceptionally gifted. I had to set up a system of two equations in two variables to get it.
Gifted? Maybe but you don't need to make 2 equations
7 + ❤ + ⭐ = 40
❤ + ⭐ = 33
For a 12-13 year old perhaps not. For a 9 year old to figure that out would be exceptional.
@tariqoner4678 I regret to inform you that what you have replied is, indeed, 2 equations. I would still consider this problem easy for a 9yo, it's just so simple.
@@ImpKraken dude, what kind of Xavier school for gifted children did you go to? The average 9 year old is still trying to wrap their head around fractions and decimals being the same thing. The word 'equation' has probably never even been said to them.
@@ImpKraken Oh I haven't noticed lol.
Interesting, I don't recall ever doing these. Took me awhile to figure out the rules pausing at the start. My approach went back to my old-school engineering days: 2 unknowns -> Create 2 equations.
I did 7 + 2 * star + 9 = 40 and 9 + star = heart. Use the first equation to get star = 12, second equation to get heart = 21.
I think they're pretending to be baffled just to get views on their posts.
Do not be discouraged by something that seems impossible. In the first triangle you can figure out a rule: base corner plus star plus heart equals top. Works with the mirror combination too. Change the numbers in the base, and you'll notice that the rule stands. Then apply it to the puzzle.
Don't be a stuck-up mathematician. Open your mind. Then, if you care, formalize your findings. But I think the main purpose of the quiz was to train young minds into being open, into becoming nimble. It's not too late for parents to take advantage.
This is a problem that should not be given to kids. All it will do is result in frustration, turn them off to math, and is really just a waste of time.
Found an alternative method that a 9-year old could use as well:
We can assume that the corners (7 & 9) are still a part of the top, (40) so we could simplify by combining the bottom corners into (16) and subtract it from (40) that will leave us with the value (24) to be used as various possibilities for Star.
We could brute force it and count down rather than count up, but we could also test by distributing the value equally across the Blank and Heart, halving the value for (12) for the same conclusion of [33]
I just brute forced it lol
Most kids younger than 12 min can't brute force it.
A quick adjustment when using the guess and check method:
After your first guess, the remainder of the total of the middle values subtracted from the top value, divided by 2 is the amount needed to add (or subtract) from the bottom number.
Your example = (40 - 18) / 2 = 11 , so 11 + 1 = 12
Way too long for a trivial problem
Maybe because MYD was exploring other solutions?
@@stigmontgomery7901 oh I always appreciate the “here’s three ways” as sometimes seeing a different solution approach helps for a completely different problem, or just understanding how people can see the world differently. But as commented elsewhere the top number is left + 2*middle + right of the bottom row. In this case I’m not sure other approaches added much insight.
Idk why did I think of this but
40-7-9 = 24
24/2=12, so ⭐= 12
And ⭐+9 = 💟 = 21
So 💟+⭐= 21+12= 33
I tried this before watching.
My thought process:
Left triangle gives rules for calculation:
- bottom right + bottom middle = middle right
- bottom left + bottom middle = middle left
- middle left + middle right = top
Using that:
- 40 = blank + ❤
- blank = 7 + ⭐️
- ❤ = ⭐️ + 9
Therefore 40 = 2⭐️ + 7 + 9
2⭐️ = 40 - (9 + 7)
2⭐️ = 24
⭐️ = 12
If ⭐️ = 12, ❤ = 12 + 9
❤ = 21
Then ❤ + ⭐️ = 33
(Also Blank = 19)
My solution was:
40 = heart + x
Heart = x + 2
40 = x + x + 2 = 19 + 19 + 2
Heart = 19 + 2 = 21
Star + 9 = 21
Star = 12
12 + 21 = 33
"Pause to Solve the Problem" Me: I solved it before I clicked the thumbnail....
It’s been over 40 years since I did algebra so I solved it by trial and error but it was good to see algebra revisited
An easier way to think about it is that the top number is always the sum of the bottom row, counting the middle number twice. So 7 + 2x(star) + 9 = 40 so (star) = 12.
Achieved solution 42 seconds into the video. I understood the first pyramid before you explained the rule, which made the second pyramid easy. Subtract the two numbers at the bottom from the top. Divide the difference by 2. The remainder is star. Add remainder to the number under heart, and the sum is heart. Add remainder and number under blank to fill blank. Add blank and heart to prove.
I did it the last way, but forgot that i was just looking for the sum of star and heart, not the individual values of star and heart, so i proceeded to solve them as well.
Pausing at 0, I think I solved it without any extra instruction. Star is 12, and heart is 21. Answer is 33. If correct, I based it off of the first triangle, where 13 can only be added up to by using a corner piece, the middle piece, and the opposite side piece of the corner piece to get the top piece's sum.
So 2+4 is 6, +7 is 13. And 3, 4, 6 is also 13 from the opposite side. The middle sections are found by adding the left corner and middle bottom together to get the left middle piece, and same deal with the right side.
So now the star and heart.
Work backwards. 40 - 7 is 33 (irony?) 40 - 9 is 31. So we need 3 numbers that fulfill the missing parts of that missing sum.
Since we know that the corner pieces must be started with, and the middle rank is (seemingly) always high in number than the bottom rank, then the bottom rank can't have a very high number in the middle. But which side to start with? Since we are missing all the 'middle pieces' so to speak, we start with the left side. Why?
Because all we have to do is ask ourselves, "what number allows us to split the 33 up so that the bottom number is still going to be lower than the middle rank numbers?"
Well, it can't be 8, because that would be lower than both the corner numbers, and the middle bottom of the left triangle is larger than the corner numbers. So it probably needs to be larger too. So it can't be less than 10. But how to find out if it's the right number?
Easy. Add the 7 to 10, to get 17, then add 19 (9 +10). If you get 40 (you won't), you got the right number. It was not the right number, the result is 36. So we're missing 4 digits somewhere in that chain. Okay, let's add 2 then, because 1 probably won't be enough. So now it's 7 + 12 = 19, and 9+12=21. Sum is 40. Okay, so we have the star, and the empty space filled. So now the heart. Well, 9+12=21, so heart must be 21.
12+21=33
This might not be the 'right' way to do it, but I got the right answer, right?
This took me, maybe 3 minutes to solve.
Another approach could be that the numbers on the middle row are going to be always with a difference of 2. Then we can ask what two numbers, with a difference of 2 between them, add up to 40? Divide 40 by two, and add and subtract 1 to each side. The answer gives you "heart" and "blank". Having those, you can easily get "star".
But I liked your third approach more.
For simplicity of explanation, let's call the star x, the heart y, and the blank space z. So, z=7+x, y=9+x, and 40=y+z, which can also be written 40=(7+x)+(9+x), which simplifies to 40=16+2x, which we can solve to 24=2x and then to 12=x.
Now that we know x is 12, we can find that y is 21 (12+9) and z is 19 (7+12), and thus x+y (or star+heart) equals 33.
I don't even teach math, I'm an English Language teacher.
We can use this approach, we'll take the top number (40 in this case as an anchor). Third rows 1st+2nd+2nd+3rd element sum should be equal to 40 as in the third row middle element is getting overlapped once. So we can say 2nd element= (40-7-9)/2 = 12 now heart= (9+12)=21. Heart+star=33
My first instinct was to notice that the number on top is the sum of the middle level, and the ones in the middle are the sum of the bottom level with the middle number twice.
So 40 = 7+2x+9
40-16=24
24/2=12.
Star is 12 and we can just work upward from there. 9+12 is 21, and 7+12 is 19. 21+19=40.
It's actually hard for a 9 year old but for an adult? Unacceptable.
I could not think of a way for a 9 yo to solve this problem. No algebra for sure. Went through the entire video. Very very interesting to see how they could solve!
Okay, so there was a much faster way
I could’ve racked my brain more
☆= 12
12+9=♡
7+12=19
♡+19=40
♡=21
Meaning:
12+21=33
An alternative approach is to think how to sum up to 40. The equal share would be 20+20, but this would require the two bottom corners to be equal. They have a distance of two and this distance needs to be kept in the middle row, because both will get added the exact same number (the middle bottom field). Creating the gap of two leads to 19 + 21, so we already have heart. And from there getting star is easy.
I was looking at the thumbnail and kind of quickly realized that 2 and 4 are below 6, and 4 and 3 are below 7. Once I got the pattern from that it was simple. I added 7 and 9 to get 16, then added 24 to get 40. and since the number at the top will be the bottom left, bottom right, and bottom middle (times 2) I could solve for star as 12. (or half of 24). after confirming what I had deduced, I then solved for heart being 21 (12+9) and from there, star + heart = 33
I'm pretty happy with myself for solving this.
0:56 Reckon ♥+⭐=33.
First lets get rid of the Emoji for the sake of my sanity and get some PROPER variables in there.
If we label the pyramid top to bottom:
♥=C ⭐=E
[A]
[B][C]
[D][E][F]
These are the rules of the Pyramid.
[A] A=B+C
[B][C] B=D+E C=E+F
[D][E][F]
We can rewrite this into an equation.(Mind you I'm not completely sure of the right way to notate this...)
[B] [C]
(D+E)+(E+F)=A
Now let's enter the variables we know.
D=7, F=9, A=40
[B] [C]
(7+E)+(E+9)=40
My first impulse is to combined like terms.
E2+16=40
Then we can cancel out the 16 by subtracting it from 40.
E2=24
Then we can cancel out the two by dividing by two.
E=12
And we can plug that into the original to check our work,
[B] [C]
(7+12)+(12+9)=40
[B] [C]
19+21=40
and it does. So we can plug all that into the Pyramid.
[40] A=19+21
[19][21] B=7+12 C=12+9
[7][12][9]
C+E=
21+12=33
Legit thought this was gonna be a compilation of questions that adults struggled with instead of just the one in the thumbnail. I solved this in well under half the time and I was terrible at maths as a kid. The method you used overcomplicated a very simple question.
7 and 9 are separated by 2. Therefore the resulting numbers in the middle row, being the sums of each number, added independently to star will be separated by 2. I divided 40 down the middle and removed a 1 from column 'a' and added it to column 'b'. I then subtracted the corresponding numbers from the bottom row to solve for star.
any arbitrary sequence of numbers can have observable patterns, but that doesn't mean you can continue the sequence based on the observed pattern unless the rules of the pattern are specified as part of the problem. many such cases
Start at 20+20 in the middle row and work in opposite directions along the number line.
Personally I found that the number in the bottom middle is used twice to make the number at the top, and the outside numbers used once.
So I subtract 7 and 9 from 40 to get to 24, then divide that by 2 and then have 12 in the bottom middle.
From there we can work out the 2 numbers above it by simple addition. getting 19 and 21. We can check that 19 and 21 add up to 40, so we know all numbers are correct. Then we can add 12 and 21 for the answer of 33.
It’s kind of easy. Just takes a second to work out the mechanics. Each layer feed into next. Total for each row will end up being Lt + 2*Mid + Rt from bottom row, since Mid gets added into both Right and Left in second row.
So 40 = 7 + 2*mid + 9
Mid = 12 = Star
Heart = 9+ Star = 21
Star + heart = 33
The only difficulty is to figure out that the absence of symbol in the left of the second raw isn't equivalent to 0. As soon as you name it x, there no longer any difficulty. Most of this riddles build upon intentional wrong formalization.