Getting a lot of comments about this so I wanted to pin a comment regarding the 'minimal puzzle'. A lot of people are asking why 80 isn't the max number of clues for a minimal puzzle or 79, or 78 or something). For the puzzle to be minimal, you need to be able to remove ANY of the given clues and be left with a puzzle that has more than one solution. If you have 80 clues you definitely have a single solution, but if you remove one then you still have a puzzle with one solution, thus not minimal. If you have a puzzle with 78 clues then it IS possible to remove one and be left with a puzzle that has 2 solutions, however you have to be able to remove any clue, it can't just work with a few of them. That's why the maximum number we THINK is 40.
Here is a reason why the Euler Brick problem would not be solved. a2+b2=x2 a2+c2=y2 b2+c2=z2 a2+b2+c2=d2 What they didn’t say is that, through manipulation, 2d2=x2+y2+z2 and the thing is that square root of 2 is irrational, and so it would be hard to work stuff like that.
Other way to think about that is, what is the maximum amount of clues you can give and still have more than one solution. Add one to that and you will have a minimal sudoku I guess.
@@datguiser so sqrt(x^2+y^2+z^2) also has to be irrational (a multiple of sqrt(2)?) For this to work. I may be wrong, but it seems to me that x^2+y^2+z^2 is a non-perfect-square power of two.
Zach Star i actually did that 41 puzzle you showed on screen at 10:28 and got more than one solution but i don’t know if that was the point of it or if it was supposed to be minimal
You can easily take this to infinity though... If the number line ranges from 0 to 1, you just put point number n at (n-1)/n + epsilon. Of course, you end up crowding points in very close near the right side, but nobody ever said they had to be equally spaced. I may be missing a constraint of the problem.
2 years into my electrical engineering career, and can say that this is false. My Configuration Manager is a woman, and I still visit my mom from time to time.
@@snifferrr Im sure that with the distance of solution, that the circle is a part of the line marked as a begining and endpoint to clearify the distance
Anti-Science is on the Rise. Uneducation causes Muffled Logic to be be more and more accepted, so casual B.S. is getting more and more popular. People embarass themselves all the time now by claming NASA is faking the Sun, the moon is a hologram, the Earth is flat, Aura and Chakra are kinda Science, so trust me bro, i know we are all immortal - oh, and one last thing: Koalas are Fake; they are ALL CGI. All.
@@Solrex_the_Sun_King That's Matt Parker, channel name "standupmaths." Also makes frequent appearances on Brady Haran's Numberphile channel. Look up, "Parker Square" for the reason for the main comment in this thread. PS: I forget whether the Parker Square video is on standupmaths or on Numberphile. Fred
The thing that surprised me is how casually you mentioned a²+b²+c² as equalling d² to find the diagonal of the box. I suppose it makes sense that it simply extrapolates Pythagoras to the 3rd dimention, but I've never seen this equation before.
@@gf1006 it’s really not though? like you can generalize the pythagorean theorem to any number of dimensions by adding another +x² term (like a² + b² + c² + d² + e² + … = h²) . that’s actually how you figure out the length of N-dimensional vectors
Edit: The channel name has now changed! For those just coming across this video, this channel was called MajorPrep but now is just my name (all majorprep related links still work though). Hey guys! Gotten a few comments about this already so I’ll just address it here. This will be the last video put out under the name ‘majorprep’, channel name is changing in about 5 days (right before the next video is released). This video was supposed to be out New Year’s Eve but there was a delay which is why I had to push back changing the channel name just a bit. Enjoy!
Yeah that and the fact that if you shuffle a deck then you likely have come across a combination that has never been shuffled before, very mind blowing to me. I learned that a while ago though and guess I was just focused on things I learned recently.
@@abijo5052 As long as you use a proper method of shuffling (spreading all the cards, moving them around, and putting them on a stack is the simplest one), yes, yes it's true. After all, a proper method of shuffling means you (almost) randomly take one of the 52 factorial ways of ordering, and 52 factorial is about 80658175200000000000000000000000000000000000000000000000000000000000. Which, for the record, is about 20000000000000000000000000000000000000000000000000 times more than the amount of seconds that have passed since the big bang (which is about 4000000000000000000 seconds).
@@abijo5052 Huh, I think YT deleted my comment for spam due to the amount of zeros I put into it. EDIT: Oh, it didn't, YT was just messing with me and not showing the comment. Anyway, you have two comments now. Anyway, yes, if you shuffle your cards PROPERLY (that means any method where there's significant variety in how the cards end up being ordered simply through the movements you make, the easiest way to ensure this is putting all the cards on a table, spreading them, shuffling them around, and then putting them back on a stack), it has a very high chance to be a unique method. 52 factorial is almost 10^68, which is about a quintillion (a billion billion) times more than the number of atoms that together make up earth. Like, you can mess up your proper shuffling badly enough to lose 20 factorial (meaning 20 cards are guaranteed to be in an order you have seen before) and you still have (to use the previous comparison) more options to order the cards than there were seconds since the big bang. The amount of seconds since the big bang MULTIPLIED BY the amount of seconds since the big bang options, to be precise. Well, and then again some ten times as much, but we don't count such little differences.
There is more chance of the atoms lining up and your hand passing straight through a table than shuffling a deck and getting a combination that someone else has already shuffled
Wow. The "connect the dots without leaving the circle and without intersection" one really sparked my interest: even without knowing about omeomorphic transformations (aside from really superficial facts), it hit me. I feel there is something deeper about thought processes in general, not only "strict" mathematical reasoning. Very beautiful
Not all rules and conditions of this puzzle were intuitively given by the thumbnail. Namely, by "line" we intuitively assume "straight line" when the solution is merely about nonintersecting _paths,_ in which case there are actually multiple possible solutions. Mine for example: - Start drawing paths from D,A,C on the lower left edge, each of them circling clockwise around point B near the center. Paths D and C will connect to their endpoints while path A must emerge between them (and continues onwards). - Now draw paths with A and B as a pair, each circling counterclockwise out of the center. Path B connects to B on the edge, with path A on the correct side of path B to continue onwards and connect to point A on the top edge.
That first one, the smart ass in me came out, you can’t “leave” the circle if you don’t enter it in the first place, the A line would just go on the outside
About cards 1. The suits come from the Tarot deck: swords->spades, wands->clubs, coins->diamonds, cups->hearts. They are not based on the seasons. 2. There were originally 14 cards in each suit. In addition to the Knave(Jack), Queen, and King, there was a Knight. 3. The jokers are remnants of the original Trump suit of 21 unique cards. So all the coincidental numerology you mentioned is just that-coincidence. If you look for such things you can easily find them anywhere. Humans create patterns where none really exist - constellations are an example. Stars of different brightness scattered across the night sky, and humanity joined them together in arbitrary patterns then assigned them arbitrary meaning (even the lines making up the "dippers" don't look anything like bears). Humans are pattern seekers, and tend to ignore data that doesn't match the pattern they decide to see.
I decided to see 13 cards in a suit, which is for 12 moons in a year with a spare for when there is 13 full moons. I like it can be used as a calendar. That it is not supposed to be is just more ingenious.
and where do you think the tarot suits come from? i can accept that 13! averages out to seven days per 52 is possibly somewhat coincidence, but the fact of the matter is that celestial clockwork was a driving or inspiring factor throughout all early cultural history until electrification.
@@TheJacklikesvideos the suits came from the Mamluk swords, coins, myriad(cup shape), and polo sticks, representing military, mercantile, spiritual?, and sporting. But the suits originated from chinese cards where the suits were: Cash (coins) -> coins/diamonds Strings of cash -> polo sticks/clubs Myriads of strings of cash (10 strings each) -> cups/hearts Tens of Myriads of strings of cash. -> swords/spades And the chinese cards were 1-9 in each of 3 suits (27 cards) possibly with 12 or 13 in the 4th suit (39-40 cards) if there was a 4th suit. The 1-9 in 3 suits continued to Mahjongg. It is interesting to look at this and realize how much changed based on there being only symbols on the early cards. As the cards moved westward, the images got reinterpreted, then redrawn, just like the game of telephone.
The paths in a disc problem is also easy if you just realize that path A divides the disc in two. For all pairs of path endpoints, keep them on the same side of path A (i.e., the same segment of the circle), then realize that no other path cuts its containing region into multiple pieces, so you can just connect your remaining endpoints in turn, in any order you want.
I love how while you were explaining the euler brick i was wondering about if there was also a solution which included(the not previously mentioned) d. I was surprised that this was the problem, and how it wasnt solved yet.
The letters on the circle puzzle is fun. It's similar to a game called "Flow Free" which contains colored pairs of dots on a grid. You have to connect the pairs without crossing lines. Puzzle sizes and number of pairs varies as the game increases in difficulty. Very addicting.
@@kyyay-yt Did they remove their comment about being unable to leave the circle? If that's what was removed, then yeah it doesn't affect what I have said. By me connecting point B to B and D to D in a straight line, there is a small gap between said straight lines which means A can be joined to A and C can be joined to C by long curved lines.
5:41 I found it amazing that the placing points in a "rectangular region" puzzle extends all the way up to 17. I would have guessed it would break down below that.
Surely someone must have thought about generalising the problem to further dimensions. But since the existence of a peefect euler brick is still unsolved, I doubt one can prove the existence of a 4 dimensional brick
Each of the ‘faces’ of a 4D Euler brick would be a 3D Euler brick, so my instinct is you’d have to prove the 3D case first. Unless you define a 4D Euler brick in some other way... Unsure what other definition would be reasonable for a 4D case.
Everyone: *Talk about everything after **0:15* Me: *Spends 20 minutes fiddling with 0.25x speed to figure out that card sorcery.* There is no frame with the card flying so I conclude that we must find this guy and burn his house 😂 JUST KIDDING.
Sweet video. I think the least compelling part was the introduction, but I'm glad I watched past that. (For reference, the intro was where you went off on a weird numerology thing with playing cards.)
Actually, it was quite interesting. Also, it wasn't numerology, but is, in fact, a historical part of how the deck of cards was first thought of and created.
Great video ,but at 1:39 you said "Lines" while they should be rather "pathes"!, in Mathematics a line is introduced to represent straight objects (i.e., having no curvature) with negligible width and depth. So the usage of Lines here instead of pathes is confusing if not obviously wrong!
To a topologist, they might as well be straight lines, since the solution will be homeomorphic to one where the dtos are connected by straight line segments. Maybe they are straight lines through a distorted plane.
Is attempts at 18 points in the rectangle using the second dimension given? For example, all the numbers line up for even splits horizontally and odd splits vertically?
Neat puzzles! I got the connect-the-lettered-dots-in-the-circle before starting the video, from the thumbnail. Same solution you got, but mine was more trial-and-error; yours is elegant. For the 5 X's along the line (or, in the rectangle), I did it numerically. Label the line 0 to 60 (the LCM of 2, 3, 4, 5), then place the points at these locations: X₁=10 X₂=50 X₃=27 X₄=40 X₅=20 I started with the last rule (fifths); then worked back up the list, making tweaks when necessary. Fred
@MajorPrep: Thanks for the 💕, and for the interesting stuff in the vid. That problem of placement of points on a line in that way, is one of those "who'd-a-thunk-it" results. 17? Maybe this'll get you promoted to Lt. Col. Prep! Fred
2:42 Mathematically this solution is defying its own rules. As these go outside of the definition of a line used in geometry. Now that’s me being very picky, mind you but it’s worth saying
@Parker Shaw A sum of two odds give an even number Despite most of the prime numbers are odd. 2 is the only even number that is prime. Hence the sum of any 2 primes doesn't really work as 2+3 or 2 + any prime number other than 2 is odd.
Just for better explanation of the problem, any even number CAN be expressed with the sum of 2 primes. There is no condition that says an even has to be expressed with a specific prime. This problem is called Goldbach Conjecture and you can find sources about it
@@drdca8263 True, it really depends on the reference point. According to Wikipedia the first ever Sudoku was printed in 1979 (however it was first popularized in 1984), so this style of puzzle is now 40 to 41 years old. Considering this, I would not claim 7 years (or more, not sure when this fact was truly found) to be "recent" xD
So, I really like his videos. They seem so relatable because this guy approaches it from an engineer's PoV while learning something new! Amazing stuff!
zach: there are 4 suits for the 4 seasons of the year and 52 cards for the 52 weeks of the year and you let ace have the value of one, then you follow from there up to 13 add up all the values and you get 364, add one joker and you get 365, days in a year add the second joker and you get 366, days of a leap year me at my 19's: *surprised pikachu* all these years and I couldnt see it.
With the Euler I was already thinking of writing a java program to find the right values but then you mentioned the 5 * 10^11. Maybe I'll give it a try some day
Circle one was easy: connect B-B, C-C, D-D inside the circle; use the circle's own circumference to connect A-A. All conditions are met! Card one was cool. There are loads of similar & more in depth explanations too!
The circle puzzle is still impossible. There is no way to do it. Lines are “line is a straight one-dimensional figure having no thickness and extending infinitely in both directions” in this case it impossible mathematically no matter what but what society considers as lines is possible. If you said something like “connect it by drawing a path then it is now possible mathematically.
I love when maths problems that intuitively seems like they should work for larger and larger values indefinitely, just randomly stop at an seemingly random number such as 17. Even funnier when that number is a really large random number, so if you brute force test it manually you'll never find a counter example, but a computer can tell you it just stops working after some millions or something.
6:08 I actually DO have a mathematics degree and I only understand the words "algebraic," "rational," "linear," and "combination," in terms of math. All of those I learned by the time I graduated high school, which suggests maybe you'd need a master's degree or have taken very specific college classes to have a better understanding of what the hell is going on with the Hodge Conjecture.
The playing card thing is purely coincidental. Spanish decks have 48 cards. Italian decks have 40 cards. German cards have 36 cards. Tarot decks have 78 cards.
As my calc teacher reminded every day, all lines are straight. Therefore this problem is mathematically unsolvable. With curves tho, easy peasy, this guy solved it!
What's is the name of the problem with N points and N regions? The one with X1 and X2 in different halves and so on... Also Can u link to a paper or something that proves 17 is the maximum?
First time I saw it was under the name 'the 18 point problem'. But wikipedia has it under a different name. Here are some links but haven't found the link to the proof just yet. Btw I found the actual problem for the first time in the book 'one hundred problems in elementary mathematics'. en.wikipedia.org/wiki/Irregularity_of_distributions mathworld.wolfram.com/18-PointProblem.html
@@zachstar I found it! www.google.com/url?sa=t&source=web&rct=j&url=core.ac.uk/download/pdf/82502278.pdf&ved=2ahUKEwj__JallunmAhXIxzgGHamiAEoQFjAAegQIBBAB&usg=AOvVaw34tS7I_5L6HXE5Hb5XmJUm
For the Euler brick, i feel like itd be easy to write a program to find one. How long the computer would take to find it, if it ever does, is an entirely different matter.
it'd actually be really difficult, if not outright impossible to even write a functional program, given the limitations of how computers store numbers. From what I understand, the only theoretically valid numbers are so large that in order to properly calculate it, you would need a very large bit integer, as memory addresses (where numbers are stored in a computer) can only go so high before it has to resort to "compacting" the numbers, which is inviable if you need exact numbers rather than rounded or numbers stored as equations, both unable to give exact, solid numbers a Euler cube needs. To explain, most computers are able to store, say, 1^1000 + 1 just fine, but having that same number in numerical form is nearly impossible, as even a 512-bit processor would overflow (the maximum storage for memory addresses are 2^x - 1, where x is the number of bits the processor uses). Since processors become exponentially harder to work with the higher bit they are, and any use for such high numbers exponentially decrease, its nearly unheard of for software to go past 128-bit. (for reference, the original NES released in 1986 used 8-bit software, and modern windows devices use 64-bit). in addition, all of this is assuming that the memory address storage is the limiting factor, which in reality is extremely unlikely to be the case past 64-bit for reasons that I can't explain without delving into a bunch of hardware and software-related content that even I'm not fully versed on.
humans cannot group more than 3 objects (to count 4 objects you group into 2 and 2 or 3 and 1, to count seven objects you do 3 +2+2, to count 12 objects you might do 3+3+3+3 but you'll never recognize a number bigger than 3 without grouping it)
there's more to the *CARDS thingy* at the beginning: There are 13 *MOON CYCLES* in a year... (i.e. LITERAL *MOON-MONTHS* ) ... Same as the number of different cards in a suit !! :P .
Card thing: very cool. Circle thing: trivial, as long as you don't start by using point A, in fact it must be last. In fact my method was exactly the one suggested, in my case I thought that there was a continuous transformation that got those points from one configuration to the other, I just had to exclude the point in the closure because those border points tend to be a pain in the butt in math. In fact my final solution was different in shape, but probably not topologically, which is what gave me the idea to use the method suggested in the video. Unfortunately, the video used the same method and I went from 'I'm smart' to 'another thing I figured out that was already figured out by others exactly as I did'. :( The line thing for 5 seemed somewhat easy, but the max number we could go I'd have no clue, for I'd need to make the solving method explore less the configuration space. 17 is definitely lower than what I'd expect. The Euler Brick problem does sound like something impossible...
Do you have any advice for people like me who started studying engineering a little late in life? Once I finished high school, I had to start working, could only start biomedical engineering at 27 years. This year I get my major.
Your videos are great! Please, make more videos about problems that you solve using mathematical logic or clever transformations or clever handling e.t.c.
1'35 I solved the original circle puzzle by using curved lines. The rules say that lines cannot leave the circle or intersect, but it did not say they had to be straight.
The fact that most puzzles are puzzles with unique solutions can sometimes give you a clue about the solution. In Sudoku, I think it manifests something like: "If I put a '3' here, then these four squares must be 1, 2, 2, and 1, or, 2, 1, 1, and 2 - but, that means there are two solutions. So if there's certainly a unique solution, I cannot put a '3' here.". I think there's even a strategy which relies on the 'minimal' aspect, like, "If there's a '2' here, then it turns out I didn't need for that '1' to be filled in at the the start of the puzzle. So, if I assume this is a minimal puzzle, without any needless extra squares filled in at the start, then there's no '2' here.". The kind of configuration where this is a useful tool is really rare, as I understand it, but I believe I saw an example once, though I can't find it again.
For the half to thirds to fourths puzzle, you could divide the area horizontally or even diagonally if you want, which would probably open up a lot of potential 😙
I love this channel! My very first passion was physics and astronomy but couldn't follow it at uni. Got a language and politics degree instead 😑 Now I've forgotten all I learned in the past, but still enjoying this so much🥰
On the one with the circle, you can draw a line going from A to A outside the circle. The first rule states the line can't "leave" the circle. With both As on the edge of the circle the line outside is never inside the circle to leave it. Also there is no rule stating you have to draw all lines inside the circle to connect them.
What if every space in the Sudoku puzzle had a satisfied number, except for one that remained open? Could 80 then be the maximum in specific conditions?
@@ryannoonan5518 It's easy to see why 80 is impossible. Removing 1 from 80 means 79 filled squares and 2 empty squares. To have two solutions, the two numbers used to complete the two empty squares must be different and interchangeable. But that cannot happen because the number that belongs to each square must be the 'missing number' either across or down (e.g. if one of the empty squares belongs to a row that contains all numbers from 1-9 except for 7, then 7 MUST be the missing number that completes that particular square and hence that 7 cannot be interchangeable with another number like 3 or 5 or anything else). Hence with 79 filled, there is only one solution. But with only 50 filled it's harder to tell since there are so many variables that complicate the problem. That's why it's still kinda unsolved
@@luvsYuri This seems really easy to do with 77 then. Create a board where the four open spots are a 2x2 area and the missing numbers are two 1's and two 2's. Make the two 1's in opposite corners and the two 2's in opposite corners. Then make two of the numbers in one square and two of the numbers in another square. Now both the rows, columns, and squares have a 1 and a 2, but you can switch the 1's and 2's and it will still be fine.
Getting a lot of comments about this so I wanted to pin a comment regarding the 'minimal puzzle'. A lot of people are asking why 80 isn't the max number of clues for a minimal puzzle or 79, or 78 or something). For the puzzle to be minimal, you need to be able to remove ANY of the given clues and be left with a puzzle that has more than one solution. If you have 80 clues you definitely have a single solution, but if you remove one then you still have a puzzle with one solution, thus not minimal. If you have a puzzle with 78 clues then it IS possible to remove one and be left with a puzzle that has 2 solutions, however you have to be able to remove any clue, it can't just work with a few of them. That's why the maximum number we THINK is 40.
Zach Star yass queen
Here is a reason why the Euler Brick problem would not be solved.
a2+b2=x2
a2+c2=y2
b2+c2=z2
a2+b2+c2=d2
What they didn’t say is that, through manipulation, 2d2=x2+y2+z2 and the thing is that square root of 2 is irrational, and so it would be hard to work stuff like that.
Other way to think about that is, what is the maximum amount of clues you can give and still have more than one solution. Add one to that and you will have a minimal sudoku I guess.
@@datguiser so sqrt(x^2+y^2+z^2) also has to be irrational (a multiple of sqrt(2)?) For this to work.
I may be wrong, but it seems to me that x^2+y^2+z^2 is a non-perfect-square power of two.
Zach Star i actually did that 41 puzzle you showed on screen at 10:28 and got more than one solution but i don’t know if that was the point of it or if it was supposed to be minimal
*Perfect this is exactly what my procrastinating brain at 3am needs.*
Anushka Uniyal bro 3am in my city and i have a lot of homework to do, and I’m watching this, totally feel you bro
@@FranciscoGonzalez-hz2bn Bueno Diaz ! "It's a her" Anushka is a lady. Indian
That's 5am for me and no, I'm not a morning person.
Literally me
Anushka Uniyal I am literally doing the exact same thing rn
Me: he's probably gonna say some stupid number like 17
Him: the highest we can go is 17
Me: :O
me:o
me: :O
Me: :0
You can easily take this to infinity though... If the number line ranges from 0 to 1, you just put point number n at (n-1)/n + epsilon. Of course, you end up crowding points in very close near the right side, but nobody ever said they had to be equally spaced. I may be missing a constraint of the problem.
@@notnotandrew nice method but if you try it you'll see that it does not work for n>3
I’ve had my eyes open for 10 minutes can I blink again now
No
It’s been a week, how are you feeling?
I’ve been bumping into things and I’m not sure if I’m in the right house
@@billywhizz09 you have my permission to blink again, I am sorry
omg thank you ahh that feels so good my eyes feel refreshed again now
About the circle thing with the points, easy, flow free trained me for that
lemme introduce you to a thing called piracy
Thats what I thought 😂😂
That's so true ahaha
Flow free is for the weak. I play flow free hexa
Mirian Raamat same but I finished all of them sadly
"do not blink"
me:"blinks"
*flicks the card*
me: *doesnt blink*
Happened to me aswell
How does it work?
@@ladripper47874 ruclips.net/video/MZVEJvrAcUo/видео.html
Ditto
I didn't blink but I looked to his fingers and feel like I just missed something by looking there and not the whole hand with the card
"I memorised them for this video"
Brings out a piece of paper
I was looking for this comment lmao
That's the joke
I read this as he did it
He memorized them on paper.
weedbong_ same man. I knew someone would bring it up in the comments.
Welcome to electrical engineering
Where Numbers are imaginary
And So are Women
This channel has the best nerdy stuff ever.
We share a lot of courses with medical engineers, plenty of women there ^^
2 years into my electrical engineering career, and can say that this is false.
My Configuration Manager is a woman, and I still visit my mom from time to time.
I became depressed 2 months into electrical engineering
Air Crash I'm CS, we have women 😎👍
I am a physics major and we have more women than men in my country. Too many are also bad.
Me on the circle puzzle :
"A-s are already connected"
Mhhhhhh👀
D is invetween
@@fredriklarsson1707 the line for d wouldn't touch the line for a though
@@snifferrr Im sure that with the distance of solution, that the circle is a part of the line marked as a begining and endpoint to clearify the distance
@@snifferrr The lines for the Ds and As would touch at the point D on the perimeter.
7:07 Ahh the Classic Memorization technique. Works really well when the Teacher is not looking.
Anti-Science is on the Rise. Uneducation causes Muffled Logic to be be more and more accepted, so casual B.S. is getting more and more popular.
People embarass themselves all the time now by claming NASA is faking the Sun,
the moon is a hologram,
the Earth is flat,
Aura and Chakra are kinda Science, so trust me bro, i know we are all immortal - oh, and one last thing: Koalas are Fake; they are ALL CGI. All.
Lmfao
😂😂😂
Him: shows dots in circle puzzle
Me: _laughs in Flow Free_
@I killed that beard guy No replies to your reply
@I killed that beard guy So I replied :D
@@commentor5479 no replies to your reply
@@commentor5479 so i replied
@@Phoenix-nh9kt no replies to your reply
Is an almost perfect Euler Brick called a Parker Brick?
Dunno who that is, but I’m still laughing cause I can only imagine Parker failed to make the first Euler brick.
@@Solrex_the_Sun_King That's Matt Parker, channel name "standupmaths." Also makes frequent appearances on Brady Haran's Numberphile channel.
Look up, "Parker Square" for the reason for the main comment in this thread.
PS: I forget whether the Parker Square video is on standupmaths or on Numberphile.
Fred
This comment made my day😂😂
He will never live that down
Even on other channels, there's still references to the Parker Square. 🤣
The thing that surprised me is how casually you mentioned a²+b²+c² as equalling d² to find the diagonal of the box. I suppose it makes sense that it simply extrapolates Pythagoras to the 3rd dimention, but I've never seen this equation before.
You can just do two pythagorean theorems. It's pretty cool when you learn that the pythagorean theorem extends to 3 dimensions like that.
But you always get pi
@@danielyuan9862 So I assume it extends to n dimensions.
@@ligafftheindifferent3495 4 dimensional pythagoras’ gets tricky, but it is theoretically possible - just don’t ever try it
@@gf1006 it’s really not though? like you can generalize the pythagorean theorem to any number of dimensions by adding another +x² term (like a² + b² + c² + d² + e² + … = h²)
.
that’s actually how you figure out the length of N-dimensional vectors
Edit: The channel name has now changed! For those just coming across this video, this channel was called MajorPrep but now is just my name (all majorprep related links still work though).
Hey guys! Gotten a few comments about this already so I’ll just address it here. This will be the last video put out under the name ‘majorprep’, channel name is changing in about 5 days (right before the next video is released). This video was supposed to be out New Year’s Eve but there was a delay which is why I had to push back changing the channel name just a bit. Enjoy!
What's it changing to?
@Canol Onar ( ͡° ͜ʖ ͡°)
How much prep did you undertake in making this decision? Might it have been a significant amount?
Perfect euler brick?
A=440000000
B=1170000000
C=2400000000
D=2706011826
X=1250000000
Y=2440000000
Z=2670000000
@@kaelanmick3065 No:
D*D=7322500002451854000
A*A+B*B+C*C=7322500000000000000
Surprised on how u didn’t go over how that there’s more ways u can order a typical 52 card deck than seconds since the Big Bang (52 factorial)
Yeah that and the fact that if you shuffle a deck then you likely have come across a combination that has never been shuffled before, very mind blowing to me. I learned that a while ago though and guess I was just focused on things I learned recently.
@@zachstar That's true in theory but probably not in practice-humans are really bad at shuffling cards
@@abijo5052 As long as you use a proper method of shuffling (spreading all the cards, moving them around, and putting them on a stack is the simplest one), yes, yes it's true. After all, a proper method of shuffling means you (almost) randomly take one of the 52 factorial ways of ordering, and 52 factorial is about 80658175200000000000000000000000000000000000000000000000000000000000. Which, for the record, is about 20000000000000000000000000000000000000000000000000 times more than the amount of seconds that have passed since the big bang (which is about 4000000000000000000 seconds).
@@abijo5052 Huh, I think YT deleted my comment for spam due to the amount of zeros I put into it. EDIT: Oh, it didn't, YT was just messing with me and not showing the comment. Anyway, you have two comments now.
Anyway, yes, if you shuffle your cards PROPERLY (that means any method where there's significant variety in how the cards end up being ordered simply through the movements you make, the easiest way to ensure this is putting all the cards on a table, spreading them, shuffling them around, and then putting them back on a stack), it has a very high chance to be a unique method. 52 factorial is almost 10^68, which is about a quintillion (a billion billion) times more than the number of atoms that together make up earth. Like, you can mess up your proper shuffling badly enough to lose 20 factorial (meaning 20 cards are guaranteed to be in an order you have seen before) and you still have (to use the previous comparison) more options to order the cards than there were seconds since the big bang. The amount of seconds since the big bang MULTIPLIED BY the amount of seconds since the big bang options, to be precise. Well, and then again some ten times as much, but we don't count such little differences.
There is more chance of the atoms lining up and your hand passing straight through a table than shuffling a deck and getting a combination that someone else has already shuffled
r/showerthoughts: it's free real estate
The Perfect Euler Brick is the Zero Euler Brick.
Not Your Average Nothing but then the brick can’t exist realistically so...
FpS Blitzzz It forms a brick black hole.
Ur so big brained
Or the Infinity Euler Brick
El Emeno Pea infinity isn't an integer
"Let's look at an example much similar."
_transition_
*ad begins*
"wanna go to red lobster on the way home?"
Wow. The "connect the dots without leaving the circle and without intersection" one really sparked my interest: even without knowing about omeomorphic transformations (aside from really superficial facts), it hit me. I feel there is something deeper about thought processes in general, not only "strict" mathematical reasoning. Very beautiful
Russell Teapot look into group theory
Not all rules and conditions of this puzzle were intuitively given by the thumbnail. Namely, by "line" we intuitively assume "straight line" when the solution is merely about nonintersecting _paths,_ in which case there are actually multiple possible solutions.
Mine for example:
- Start drawing paths from D,A,C on the lower left edge, each of them circling clockwise around point B near the center. Paths D and C will connect to their endpoints while path A must emerge between them (and continues onwards).
- Now draw paths with A and B as a pair, each circling counterclockwise out of the center. Path B connects to B on the edge, with path A on the correct side of path B to continue onwards and connect to point A on the top edge.
Finally a random RUclips algorithm video that is fun and within my interests.
Hi. Know Sci Man Dan? The funny education-youtuber?
That first one, the smart ass in me came out, you can’t “leave” the circle if you don’t enter it in the first place, the A line would just go on the outside
I did the same xD
I was thinking it was similar to another puzzle I've seen and just went with it
My A-A traced the circle lol
I thought about connecting on top of the circle’s circumference
About a deck of cards: I was always told that the kings are meant to be real people. Julius Caesar, Charlemagne, Alexander The Great
And the fourth one?
@@callisto5097 Genghis Khan probably
Pretty sure Genghis Khan isn't on a regular bicycle deck
francisco jimenez de cisneros, because nobody expects the spanish inquisition!
Rebecca Alderstorm bill
About cards
1. The suits come from the Tarot deck: swords->spades, wands->clubs, coins->diamonds, cups->hearts. They are not based on the seasons.
2. There were originally 14 cards in each suit. In addition to the Knave(Jack), Queen, and King, there was a Knight.
3. The jokers are remnants of the original Trump suit of 21 unique cards.
So all the coincidental numerology you mentioned is just that-coincidence. If you look for such things you can easily find them anywhere. Humans create patterns where none really exist - constellations are an example. Stars of different brightness scattered across the night sky, and humanity joined them together in arbitrary patterns then assigned them arbitrary meaning (even the lines making up the "dippers" don't look anything like bears).
Humans are pattern seekers, and tend to ignore data that doesn't match the pattern they decide to see.
I decided to see 13 cards in a suit, which is for 12 moons in a year with a spare for when there is 13 full moons.
I like it can be used as a calendar. That it is not supposed to be is just more ingenious.
and where do you think the tarot suits come from? i can accept that 13! averages out to seven days per 52 is possibly somewhat coincidence, but the fact of the matter is that celestial clockwork was a driving or inspiring factor throughout all early cultural history until electrification.
@@TheJacklikesvideos the suits came from the Mamluk swords, coins, myriad(cup shape), and polo sticks, representing military, mercantile, spiritual?, and sporting.
But the suits originated from chinese cards where the suits were:
Cash (coins) -> coins/diamonds
Strings of cash -> polo sticks/clubs
Myriads of strings of cash (10 strings each) -> cups/hearts
Tens of Myriads of strings of cash. -> swords/spades
And the chinese cards were 1-9 in each of 3 suits (27 cards) possibly with 12 or 13 in the 4th suit (39-40 cards) if there was a 4th suit. The 1-9 in 3 suits continued to Mahjongg.
It is interesting to look at this and realize how much changed based on there being only symbols on the early cards. As the cards moved westward, the images got reinterpreted, then redrawn, just like the game of telephone.
Another fun fact is you can shuffle any 52 deck of cards and you will most likely be holding a deck that nobody in human history has ever held.
@@BiggerBearnot probably you really will be holding a shuffled deck that has never been before it's the 52! factorial
This is practically the only math lesson I’m willing to listen to
Anti-Science is on the Rise. Uneducation causes Muffled Logic to be be more and more accepted, so casual B.S. is getting more and more popular.
If there werent at least 5 moments in this video where I paused and my jaw dropped to the floor, there were none
Lol
The paths in a disc problem is also easy if you just realize that path A divides the disc in two. For all pairs of path endpoints, keep them on the same side of path A (i.e., the same segment of the circle), then realize that no other path cuts its containing region into multiple pieces, so you can just connect your remaining endpoints in turn, in any order you want.
I love how while you were explaining the euler brick i was wondering about if there was also a solution which included(the not previously mentioned) d. I was surprised that this was the problem, and how it wasnt solved yet.
me at fiest: that's a video about some random silly thigs i can understand
me at 6:08 : nope,you lost me there
I hate playing cards in the White house.
The president always has a trump card.
AAAAAAAAAAAAAAAAA
Make that, "playing contract bridge," and it's even better.
Fred
But he's the joker.
Good one!
@@jayfredrickson8632 obama is the joker
What you mentioned at 02:45 is basically what thoeretical computer science lives and breathes for. Breaking hard problems into more easier problems.
I'm surprised how big the smallest side number for the perfect Euler brick is.
And that’s *if* one exists, so it may turn out to be not surprising.
Addition to the card deck:
13 types of cards = 13 week in one season
12 "picture" cards (J,Q,K x 4) = months in year
Oh what???
The design on the 8 Card makes an 8
Keep going with more random surprises!
I am feeling lucky!
The letters on the circle puzzle is fun.
It's similar to a game called "Flow Free" which contains colored pairs of dots on a grid. You have to connect the pairs without crossing lines. Puzzle sizes and number of pairs varies as the game increases in difficulty. Very addicting.
OK, I thought the first problem was simple: A and A are already connected by a line (the line that makes out the circle).
Nope
Not at all. That line pass through at least another point, and that's not allowed.
Thanks to my expertise in the game “Flow” that puzzle was cake
2:09
Why wouldn't you just connect D to D, then B to B...
...Then, just move A to A and C to C around those 2 lines?
exactly what i thought :D
@@31.vaishanavikurup20 so? this does not affect the answer the commenter has given
@@kyyay-yt Did they remove their comment about being unable to leave the circle?
If that's what was removed, then yeah it doesn't affect what I have said.
By me connecting point B to B and D to D in a straight line, there is a small gap between said straight lines which means A can be joined to A and C can be joined to C by long curved lines.
@@Serpinstrix yeah, it was that
Random coincidences that will be assorted together to look like a pattern
Sounds like one of those illuminati videos
the puzzle of cennecting ‘a to a, b to b’ and so on was easy.
i didn’t even have to move them
good for u 👏
Ok boomer
want a medal?
It's actually very easy if you just connect "a to a" last
5:41 I found it amazing that the placing points in a "rectangular region" puzzle extends all the way up to 17. I would have guessed it would break down below that.
Important: Is there any research on a 4- or higher dimension euler brick?
Surely someone must have thought about generalising the problem to further dimensions. But since the existence of a peefect euler brick is still unsolved, I doubt one can prove the existence of a 4 dimensional brick
Each of the ‘faces’ of a 4D Euler brick would be a 3D Euler brick, so my instinct is you’d have to prove the 3D case first. Unless you define a 4D Euler brick in some other way... Unsure what other definition would be reasonable for a 4D case.
Isn't that Fermat's last theorem?
nabiddy badiddy no, because whatever dimension you go in, you will only need squares and square roots to calculate lengths
@@toniokettner4821 ah yes of course you're right
a neat tabletop game called "the quiet year" uses the card deck fun fact as a core mechanic
Hearing "17" and immediately pressing like.
It appears twice!
Everyone: *Talk about everything after **0:15*
Me: *Spends 20 minutes fiddling with 0.25x speed to figure out that card sorcery.* There is no frame with the card flying so I conclude that we must find this guy and burn his house 😂 JUST KIDDING.
I did the same - I'm guessing a frame was removed.
Sweet video. I think the least compelling part was the introduction, but I'm glad I watched past that. (For reference, the intro was where you went off on a weird numerology thing with playing cards.)
Yeah he thought it's gonna capture attention but it actually repel
But I just skipped that, now everything is fine
Actually, it was quite interesting. Also, it wasn't numerology, but is, in fact, a historical part of how the deck of cards was first thought of and created.
@@roylavecchia1436 Agreed, the card thing was some interesting history behind I assume the number of cards in a deck, the number of faces, etc.
uploaded 3 years ago and it finds me on a random evening in April 2023 thanks buddy
Great video ,but at 1:39 you said "Lines" while they should be rather "pathes"!, in Mathematics a line is introduced to represent straight objects (i.e., having no curvature) with negligible width and depth.
So the usage of Lines here instead of pathes is confusing if not obviously wrong!
No wonder I was confused (totally not because I'm dumb)
To a topologist, they might as well be straight lines, since the solution will be homeomorphic to one where the dtos are connected by straight line segments. Maybe they are straight lines through a distorted plane.
@@isaacwebb7918 so, the earth is flat, but the universe is curved. which makes the line straight even though it looks bent
It is straight if you are on a sphere. Three transform is rotating a sphere so 2d projection realigned the points
Is attempts at 18 points in the rectangle using the second dimension given? For example, all the numbers line up for even splits horizontally and odd splits vertically?
Neat puzzles!
I got the connect-the-lettered-dots-in-the-circle before starting the video, from the thumbnail. Same solution you got, but mine was more trial-and-error; yours is elegant.
For the 5 X's along the line (or, in the rectangle), I did it numerically. Label the line 0 to 60 (the LCM of 2, 3, 4, 5), then place the points at these locations:
X₁=10 X₂=50 X₃=27 X₄=40 X₅=20
I started with the last rule (fifths); then worked back up the list, making tweaks when necessary.
Fred
@MajorPrep: Thanks for the 💕, and for the interesting stuff in the vid.
That problem of placement of points on a line in that way, is one of those "who'd-a-thunk-it" results. 17?
Maybe this'll get you promoted to Lt. Col. Prep!
Fred
The first connect the lines one took me a solid 5 seconds
congratulations
lulukenn _ no
@@theyumblat5420 sorry?
2:42
Mathematically this solution is defying its own rules. As these go outside of the definition of a line used in geometry. Now that’s me being very picky, mind you but it’s worth saying
1:32 was quite easy
Flow free taught me well
Any even number is the sum of 2 primes, clearly simplest unsolved.
is that really true
I'm not sure if I'm correct but
1 x 2 is 2
So 2 is the sum of 1 prime and 1 non-prime rather than 2 primes.
@@abdi165 thats a product. sum is when you add
@Parker Shaw
A sum of two odds give an even number
Despite most of the prime numbers are odd. 2 is the only even number that is prime. Hence the sum of any 2 primes doesn't really work as 2+3 or 2 + any prime number other than 2 is odd.
Just for better explanation of the problem, any even number CAN be expressed with the sum of 2 primes. There is no condition that says an even has to be expressed with a specific prime. This problem is called Goldbach Conjecture and you can find sources about it
"Recently confirmed" that you need at least 17 clues for a proper Sudoku? Numberphile had a video on that topic 7 years ago :-)
7 years ago is recent in some contexts
@@drdca8263 True, it really depends on the reference point. According to Wikipedia the first ever Sudoku was printed in 1979 (however it was first popularized in 1984), so this style of puzzle is now 40 to 41 years old. Considering this, I would not claim 7 years (or more, not sure when this fact was truly found) to be "recent" xD
MoD366 Oh! I didn’t realize that sudoku was that young. Good point!
@@drdca8263 I also expected it to be older. Good thing I checked first xD
2:14 you didn’t even have to move the points -_-
So, I really like his videos. They seem so relatable because this guy approaches it from an engineer's PoV while learning something new! Amazing stuff!
zach: there are 4 suits for the 4 seasons of the year
and 52 cards for the 52 weeks of the year
and you let ace have the value of one, then you follow from there up to 13
add up all the values and you get 364, add one joker and you get 365, days in a year
add the second joker and you get 366, days of a leap year
me at my 19's: *surprised pikachu*
all these years and I couldnt see it.
"40 is the smallest known minimal sudoku clues"
80 clues: "hold my paper"
With the Euler I was already thinking of writing a java program to find the right values but then you mentioned the 5 * 10^11. Maybe I'll give it a try some day
Yeah, and the odd edge must be larger than 2.5 x 10^13. Maybe not, for me.
Time for quantum computing!
Circle one was easy: connect B-B, C-C, D-D inside the circle; use the circle's own circumference to connect A-A. All conditions are met!
Card one was cool. There are loads of similar & more in depth explanations too!
The circle puzzle is still impossible. There is no way to do it. Lines are “line is a straight one-dimensional figure having no thickness and extending infinitely in both directions” in this case it impossible mathematically no matter what but what society considers as lines is possible. If you said something like “connect it by drawing a path then it is now possible mathematically.
Lines , Rays , segments , they’re all the same to him
I love when maths problems that intuitively seems like they should work for larger and larger values indefinitely, just randomly stop at an seemingly random number such as 17. Even funnier when that number is a really large random number, so if you brute force test it manually you'll never find a counter example, but a computer can tell you it just stops working after some millions or something.
2:50 those aren't lines, welcome to geometry.
Brady Walker Do you feel smart now?
those are lines, welcome to topology.
@@boredommm23 if by topology you mean IQ you are correct
Curved lines:
5:31 I GUESSED 17 AND I'M REALLY SURPRISED, GOOD JOB
6:08 I actually DO have a mathematics degree and I only understand the words "algebraic," "rational," "linear," and "combination," in terms of math. All of those I learned by the time I graduated high school, which suggests maybe you'd need a master's degree or have taken very specific college classes to have a better understanding of what the hell is going on with the Hodge Conjecture.
The playing card thing is purely coincidental.
Spanish decks have 48 cards.
Italian decks have 40 cards.
German cards have 36 cards.
Tarot decks have 78 cards.
moving the points in the circle isn’t just a homeomorphism, it’s an isomorphism, which is the actual property that allows the points to still connect
You're cool dude, please never stop making videos (Unless you want to lol)
Haha thanks man! Not stopping anytime soon
Politicians at 3:30 : "I can do that. Just the points wherever and I'll draw the lines around it."
0:10: **turns on 0.25 speed**
But the question is, are they lines of they're not linear?
exactly my thoughts
As my calc teacher reminded every day, all lines are straight. Therefore this problem is mathematically unsolvable. With curves tho, easy peasy, this guy solved it!
Hi. Know Sci Man Dan? The funny education-youtuber?
You're looking at a projection of a wiggly surface maybe a sphere even, so that is why transform works. Sphere projection rotates
If you shuffle a pack of cards, no pack of cards on earth has ever been in that order before
What's is the name of the problem with N points and N regions? The one with X1 and X2 in different halves and so on...
Also Can u link to a paper or something that proves 17 is the maximum?
Bro you give us a solution for 18 and you're likely to get a field prize
First time I saw it was under the name 'the 18 point problem'. But wikipedia has it under a different name. Here are some links but haven't found the link to the proof just yet. Btw I found the actual problem for the first time in the book 'one hundred problems in elementary mathematics'.
en.wikipedia.org/wiki/Irregularity_of_distributions
mathworld.wolfram.com/18-PointProblem.html
@@zachstar Thank you!
@@zachstar I found it!
www.google.com/url?sa=t&source=web&rct=j&url=core.ac.uk/download/pdf/82502278.pdf&ved=2ahUKEwj__JallunmAhXIxzgGHamiAEoQFjAAegQIBBAB&usg=AOvVaw34tS7I_5L6HXE5Hb5XmJUm
"I memorized them for this video"
- Pulls out piece of paper to copy
The one with the circle and points is actually impossible, because all lines are straight. You can use curves to get it done, but those arent lines
this comments is underrated
Why not?
@@thej3799 had to rewatch this video since i made the comment 3 years ago, but 14 yr old me was right! lines, by definition, must be straight.
For the Euler brick, i feel like itd be easy to write a program to find one. How long the computer would take to find it, if it ever does, is an entirely different matter.
it'd actually be really difficult, if not outright impossible to even write a functional program, given the limitations of how computers store numbers. From what I understand, the only theoretically valid numbers are so large that in order to properly calculate it, you would need a very large bit integer, as memory addresses (where numbers are stored in a computer) can only go so high before it has to resort to "compacting" the numbers, which is inviable if you need exact numbers rather than rounded or numbers stored as equations, both unable to give exact, solid numbers a Euler cube needs.
To explain, most computers are able to store, say, 1^1000 + 1 just fine, but having that same number in numerical form is nearly impossible, as even a 512-bit processor would overflow (the maximum storage for memory addresses are 2^x - 1, where x is the number of bits the processor uses). Since processors become exponentially harder to work with the higher bit they are, and any use for such high numbers exponentially decrease, its nearly unheard of for software to go past 128-bit. (for reference, the original NES released in 1986 used 8-bit software, and modern windows devices use 64-bit).
in addition, all of this is assuming that the memory address storage is the limiting factor, which in reality is extremely unlikely to be the case past 64-bit for reasons that I can't explain without delving into a bunch of hardware and software-related content that even I'm not fully versed on.
I literally created a new saved playlist called interesting for this video
humans cannot group more than 3 objects (to count 4 objects you group into 2 and 2 or 3 and 1, to count seven objects you do 3 +2+2, to count 12 objects you might do 3+3+3+3 but you'll never recognize a number bigger than 3 without grouping it)
I’m writing this comment to prove I was here in 2020 when this gets recommended again in 10 years
If youtube still exists then
And that’s exactly why I’m replying
there's more to the *CARDS thingy* at the beginning:
There are 13 *MOON CYCLES* in a year... (i.e. LITERAL *MOON-MONTHS* ) ... Same as the number of different cards in a suit !! :P
.
Card thing: very cool.
Circle thing: trivial, as long as you don't start by using point A, in fact it must be last. In fact my method was exactly the one suggested, in my case I thought that there was a continuous transformation that got those points from one configuration to the other, I just had to exclude the point in the closure because those border points tend to be a pain in the butt in math. In fact my final solution was different in shape, but probably not topologically, which is what gave me the idea to use the method suggested in the video. Unfortunately, the video used the same method and I went from 'I'm smart' to 'another thing I figured out that was already figured out by others exactly as I did'. :(
The line thing for 5 seemed somewhat easy, but the max number we could go I'd have no clue, for I'd need to make the solving method explore less the configuration space. 17 is definitely lower than what I'd expect.
The Euler Brick problem does sound like something impossible...
"Do not blink" *blinks immediately*
Do you have any advice for people like me who started studying engineering a little late in life?
Once I finished high school, I had to start working, could only start biomedical engineering at 27 years. This year I get my major.
Every Joker's day of a year is 137.035999 days-away from another.
Wait... I stayed for the card trick reveal~!
About the Euler Brick:
the euler brick with the smallest possible values is (0,0,0)
Your videos are great! Please, make more videos about problems that you solve using mathematical logic or clever transformations or clever handling e.t.c.
1'35 I solved the original circle puzzle by using curved lines. The rules say that lines cannot leave the circle or intersect, but it did not say they had to be straight.
My mans be lookin like he hasnt slept in 6 years
The fact that most puzzles are puzzles with unique solutions can sometimes give you a clue about the solution. In Sudoku, I think it manifests something like: "If I put a '3' here, then these four squares must be 1, 2, 2, and 1, or, 2, 1, 1, and 2 - but, that means there are two solutions. So if there's certainly a unique solution, I cannot put a '3' here.".
I think there's even a strategy which relies on the 'minimal' aspect, like, "If there's a '2' here, then it turns out I didn't need for that '1' to be filled in at the the start of the puzzle. So, if I assume this is a minimal puzzle, without any needless extra squares filled in at the start, then there's no '2' here.". The kind of configuration where this is a useful tool is really rare, as I understand it, but I believe I saw an example once, though I can't find it again.
When I saw your video with a different name channel, I thought someone else had uploaded your video
Nailed the title. All it took was thinking about all idiots that force us to not walk in a straight line.
For the half to thirds to fourths puzzle, you could divide the area horizontally or even diagonally if you want, which would probably open up a lot of potential 😙
He said it should be considered 1-dimensional
"Give that some thought, but not really cuz it's gonna take you a while.." 😂
2:40 yooooooo
I got a very similar result when I sketched it
I love this channel! My very first passion was physics and astronomy but couldn't follow it at uni. Got a language and politics degree instead 😑 Now I've forgotten all I learned in the past, but still enjoying this so much🥰
scp-173 be like:
0:07
s n a p
On the one with the circle, you can draw a line going from A to A outside the circle. The first rule states the line can't "leave" the circle. With both As on the edge of the circle the line outside is never inside the circle to leave it. Also there is no rule stating you have to draw all lines inside the circle to connect them.
What if every space in the Sudoku puzzle had a satisfied number, except for one that remained open? Could 80 then be the maximum in specific conditions?
to be minimal, it requires that removing one number from that 80 will yield a sudoku puzzle with more than 1 solution and that is impossible
bronchosaurus211 mabye it isn’t the problem is unsolved haha
@@ryannoonan5518 It's easy to see why 80 is impossible. Removing 1 from 80 means 79 filled squares and 2 empty squares. To have two solutions, the two numbers used to complete the two empty squares must be different and interchangeable. But that cannot happen because the number that belongs to each square must be the 'missing number' either across or down (e.g. if one of the empty squares belongs to a row that contains all numbers from 1-9 except for 7, then 7 MUST be the missing number that completes that particular square and hence that 7 cannot be interchangeable with another number like 3 or 5 or anything else). Hence with 79 filled, there is only one solution. But with only 50 filled it's harder to tell since there are so many variables that complicate the problem. That's why it's still kinda unsolved
@@luvsYuri This seems really easy to do with 77 then. Create a board where the four open spots are a 2x2 area and the missing numbers are two 1's and two 2's. Make the two 1's in opposite corners and the two 2's in opposite corners. Then make two of the numbers in one square and two of the numbers in another square. Now both the rows, columns, and squares have a 1 and a 2, but you can switch the 1's and 2's and it will still be fine.
bronchosaurus211 oh yeah that’s cool nice