lol ikr

Mswordx23 ??? 6700000000000000000000

Mswordx23 6,7 trilliard :p And yes we are using the extended system here.

strayster2 Correct. You can write Avogadro's number as 602.2x10^21 instead, and it should become clear that it is larger than the sudoku grids number of 6.7x10^21, nearly ninety times larger in fact.

Immortes Mortallis Yes, Avogadro's number in true scientific notation is indeed 6.022x10^23. However, 602.2x10^21 is an equally valid representation of the same number, just not the standard form. I wrote it that way to show clearly how much bigger Avogadro's number is from the number of sudoku grids by comparing them at the same order of magnitude, which is 10^21.

I only need 72

Patrick Star rly? my sudoku book doesn't give me clues.

Well you need 78 to be guaranteed unique solution, since the smallest unavoidable sets is of size 4

lol XD

Completed instantly

Lol

Yeah… now you know to check how long a program will take before you launch it! :)

The Real Flenuan Let us know if you find a way to do that

Harry Wagstaff you can easily calculate it with... you guessed it... maths...

I think Alan Turing might have something to say about that

Looked for this, found it. Thank you, carry on.

Those sudokus have additional constraints

@@QuinsonHonQBB123XX Well, yes but he wrote this for a joke :)

I miss machinarium :/

@@QuinsonHonQBB123XX then it’s not called a sudoku. They have different names. For example the killer sudoko doesn’t have clues but consists of two or more grits with the sum of the numbers in the grits, and a there are sudoku’s with tinted grits that allows only for even or uneven numbers. There are sudoku where the 3x3 rectangular is changed in all kind of forms. And all have their own name.

Grids, he just wrote the G weird

+Mr_Peak Actually I think it's C (Subscript T) RIDS

+&thony it's a test

+allnamesaretakenb4 He also says, "C, number of squids" (at least it doesn' t sound like a hard 'g' for "grid" (I know, he does not say squid, more like sqrid) But what does CtRIDS mean? (Count Number of RIDs? R=Real numbers ID as in (uniqe) IDentifier?) So the Count in numbers (real numbers) with unique identifier for every possible grid? That would almost make sense to me...

+Countryen I think it's because he was starting to say "squares" and then corrected himself to "grids". As far as what he wrote, it's "GRIDS". XD

Wow. Thanks for the info

Would the ever-reliable Bowman's Bingo work on it?

​@@samprice7746 So I found the puzzle in question (it's 800000000003600000070090200050007000000045700000100030001000068008500010090000400 as an 81-digit number) and entered into sudokuwiki's sudoku solver. It exhausted every strategy and effectively got stuck, including Bowman's Bingo.

@@ganaraminukshuk0 Yep! since commenting I've learned there are at least 5 of these, but I can't remember where they were from. I know arto inkala is a preset on that website, it's pretty cool isn't it?

@@ganaraminukshuk0 I took that puzzle to Sudoku Solutions and let it give it a go. It eventually gave up on logic and just brute forced the thing. It even admitted that it had to brute force it because there were no logical moves to start with.

77. You could have every number in the puzzle as a "clue" with the exception of 4 unavoidable squares filled in

Twilit Area Oh yeah :D thanks

Twilit Area what?

What he means is: take the example sudoku given with the 7s and 9s circled. You can swap these 7s and 9s and still get a valid sudoku, as said in the video. So if you fill in the whole sudoku except for the four circled numbers ((9*9=81 squares)-4 squares mentioned=77 squares) it still isn't uniquely solveable, since you could fill in 7-9-9-7 or 9-7-7-9, so still have two solutions. Thus 77 clues - in certain constructed circumstances - may not be enough to solve the puzzle uniquely. Now about 78 always being enough: They could all be in the same row or not (same logic goes for column). If they are, they are all in different columns, and each column can be solved by just filling in the 9th missing number. If they are not, they are divided 2-1. so this time, one is being solved as the last of a row, and then the other 2 are the only remainders in their respective column.

81

I completely agree!

How boring for you!

+Matias Kurvinen ...

+Matias Kurvinen But can you do it uniquely?

+Lepidolite Mica [SPOILER ALERT]: He can't.

Is this a comment train of trolls or does nobody get the joke?

Not uniquely, though...

To be fair, mathematicians are being paid to do this. If I got paid to watch TV or play video games and didn't have to worry about things like whether or not I'm providing useful information (like reviews) and don't have to be entertaining (like a let's play) but just have to do some trivial thing that helps no one, people would wonder what my employer is thinking.

But also to be fair, some of the things we'd think were completely useless or even imaginary (like the Turing machine) are the precursor to incredible game changing inventions like the computer. We wouldn't have computers were it not for mathematicians so who knows? Maybe the methods used to solve this Sudoku problem will help us with the next age of technology.

tanukigalpa I know, that would be the answer to the the question of why they are solving seemingly useless things. I was just defending asking why in the first place.

Max Đỗ that's a false equivalents. people waste their time and wonder why/how someone can get paid for something that appears as if it's also a waste of time. it's really cool that this guy explains how it may become valuable at some point.

It's more the fact that they're paid.

"It's like a joke! It's not much like one, I'll give you that."

Bit of a Parker joke then

I was wondering the same thing.

probably it will have many solutions, but there are some 17 clue ones that only have 1 solution, but there are none that have 1 solution with 16 clues

how can you tell?... you try to solve it...

Just because I can't solve it does not prove that no solution exists.

At this point you should just be able to brute force it - look at every possible way to fill the board and see how many of them work. If it's just one, congrats, it's a unique solution. And if you already have a solution proving uniqueness is even easier: if you only followed logical deduction to obtain it and got a full board, there is no way a different board is possible.

They are being paid for doing this things, and using thousands of the best computers for almost a year isn't free either. I think that asking why are they doing this is a legitimate question.

@@freshrockpapa-e7799 yes but this is paid by the University not your taxpayer money so why do you care haha

Michael from VSauce made a great point about the human nature of pushing every boundary just for the sake of it in his Supertasks video

I thought you were asking a question when you used a question mark. Also, it's written "thought".

I believe you lost an "R" there.

CTRIDS

Seppuku, bakaru!

Christopher Ellis, they used to require seppuku, but in the 80's we came up with the more humane solution of requiring sudoku (for dishonoring one's own family) :P

Do you watch Dave Gorman? In an episode on puzzles he pointed out there were books with forbidding names like Ultra Killer Sudoku and even one called Hara Kiri Sudoku, thus missing out on an opportunity to call the book Seppuku Sudoku!

Why bother? Many words can, phonetically be spelt in many ways. Why not klew; cloo; clu; clugh. If there is already an established spelling why not stick with it? more people will understand what you're trying to say.

Tadashi Mori You have to keep in mind that 17 is not a constant. Not every sudoku has the minimum of 17 clues, some need more clues. Knowing that you have to ask which sudokus need 17, which ones need 18 clues and so on. What is the constelation for a certain minimum of clues? Can you even categorize the sudokus which have 17, 18, 19 etc. minimal clues? I guess it's not as straight forward as you might think.

There is an idea out there proposed by Mcguire that you can calculate the smallest critical set from number of solutions for general sized sudoku (the typical one is 3x3), this idea is shown to fail for latin squares larger than, but is true for all sizes of sudoku where the smallest critical set is known.

Funny thing is, I'm pretty certain that if you fill a row and a column with these clues, it would guarantee that your sudoku wouldn't have a unique solution. Am I seeing this wrong?

Chanter Ex: Absolutely. Here's the proof: if you could have a unique solution by only filling a row and a column with the minimum 17 clues, then you would have the same unique solution if you removed any of those clues (the last number to fill a row, column or square is defined by the other 8). And therefore you would have a unique solution with only 16 clues, which was just proven to be impossible.

It's an Irish Computer! I gather that none of you have had much to do with Sūdoku. You'd know better than to believe this

Exactly. "Sudoku" was essentially a trademark name that got genericized.

OK, kinda late, but here's... something: -First af all, you need to realize that the reason the sum of the digits of the final number equals 9 is because the number is divisible by 9, and it just happens that any number divisible by 9 will have its digits sum a multiple of 9 (and you can sum that number's digits to get another multiple and so on until you get to 9) -We'll split the substraction in two parts: substracting the rightmost digit, and substracting all other digits. By doing the first thing, you're effectively rounding the number down to the nearest multiple of 10. We'll do the second thing later. So here's the explanation for 2 digits, where you can even do more awesome stuff than just divide by 9: -So, now the number is divisible by 10, meaning that you can divide it in 10 equal parts. So if we remove 1, the number will be divisible by 9. If we remove 2, the number will be divisible by 8. -This is the reason this works with only 2 digits, because the first digit didn't count at all, all you have is the second digit (the 10s digit), wich you're effectively dividing by 10 when you substract the digit. I might've not eplained it too well so here's an example: Take the number 76, what you'll do is 76-(7+6), wich is the same as 76-6-7 wich is 70-7. 7 is 10 times lower than 70 because you're moving it from the 10's. Meaning that now you've reduced the number (70) by 1/10th. Because we know the number was divisible in 10 equal parts, by removing one the result will be divisible in 9 equal parts. If we remove another 7, the number will be divisible by 8 and so on. But that didn't solve the problem for all number of digits. Maybe i'll do that later, but it probably has to do with the sum of the digits of multiples of 9 being 9

0. Just make your own grid.

I would say that rule, dramatically, decreases the number of possible grids. Still solvable, and with a unique solution if 17 clues are given, but the total number of possible grids wouldn't be as big as 6.7E21

in that version, you can have fewer than 17 clues and still find the puzzle solvable.

i am not sure you are right on this one, given that the diagonal rule would make row/column switching illegal, which was the biggest way to make families.

+Nick Roethel being a mathematician implies the disability to spell, but not the other way around!

+Henry Jun just a joke dude. Just because someone is a mathematician (or any other ician or ologist) doesn't mean they're bad spellers.

@@dcngn_ haha.

+chakor pandkar He said what the families were in this one. I don't think it'd be enough to validate another full video, but I'll see if I can explain it for you a little better. 'Families' as he was referring to are sets of puzzles with matching Rows or Columns. So it was basically the same puzzle, just rearranging the Rows or Columns, which keeps the puzzle valid.

Cool. Thanks. Hey i suggest u also do a video explaining the no of dimensions. I saw something on the net saying that there are multiple dimensions that ia proved through maths. Id love to see such content. Or even unsolved puzzles that have not been yet solved.

+chakor pandkar Wikipedia has articles on several problems that we don't have satisfying answers for, especially in the realm of formal logic and probability. If you want to learn more about higher dimensions, look up tesseracts, or watch Matt Parker's "Things to See and Hear in the Fourth Dimension".

That's easy to do, if you put 1,2 in the top left square, then 2,1 in the square below that, then 1 above 2 in the bottom middle square and 2 above 1 in the bottom right square, then you can't place both 1 and 2 in the bottom left square.

I figure all these 1s and 2s wouldn't be subtle enough.

***** This is true... can I change my order?

***** hmm, yes that was phrased rather poorly wasn't it? I meant change the question, I suppose? But it wasn't a question to begin with... change the thought? Basically revise the original statement to: "I wonder if there's a way to give a specific layout of clues that's impossible to solve, yet subtle enough that you can't tell?"

***** Or, for one of the fives, work it so that the only number that could be there is a five, so it doesn't look like they line up.

it's 78

It's definitely less than that. It would have to be no greater than 64, and it would definitely be less than that as well.

David Davison Nope, 78 is correct. If you look at the full grid shown in the video and turn it into a puzzle with all squares except for the two 7-9 pairs included as clues, you have a 77-clue puzzle without a unique solution. You would need at least one more clue to solve this grid uniquely, therefore the answer is 78.

Thats like saying you no longer enjoy playing soccer because you invented a robot that plays soccer. Your code doing it isnt you doing it!

David Sharp If it becomes procedural, it's not interesting. Soccer wouldn't be procedural even if you had programmed a robot, because there's far too much to a physical sport than just some simple logical deduction.

Watching soccer =/= playing soccer

Agreed. What's you point? *Playing* soccer is far more in-depth than a Sudoku puzzle which consists of nothing more than simple deduction and simple motor skills to draw numbers.

SpiderWick12 "What's you point?" It's funny that you say this when you didn't addressDavid Sharp's original point and knocked down a straw man instead. If you fail to see how you succumbed to the logical fallacy, you probably shouldn't debate with others.

permutation/combinations

+SkydiverTyler I bet it's 2n-1

Kavukamari well a 4*4 grid would be 4*2-1=7. So, possibly

+SkydiverTyler No it is not 2n-1. the 4*4 grid below has only one solution but 6 clues : 4 x 1 x x 1 x x x 2 x 1 1 x x x

if you play on 4*4 grid you play with 4 numbers and there are 2*2 boxes instead of 3*3 boxes

Rubik's cube.

@@ericstoverink6579 but that's so EASY!

Yeah, it isnt even true that the japanese name stuck... In japan the word for sudoku is "namupure", which is actually a corruption of "number play" rendered in japanese katakana script as "namuba purei" and shortened to namupure. Truth is, sudoku and the game being japanese is just marketing gimmick in the west... And giving it a western root name in japan is also just a marketing gimmick. Still, they are fun eh.

So does "Sudoku" actually mean anything in Japanese? If so, what?

You just divided by zero.

dapsize01 So...I broke mathematics.

+Robert Andersson Is the curve half 3 or a quarter 8?

+Robert Andersson whoa, 3/4 clue of an 8 would make it 9 or 6.

MasterBata Yes, you are right. ☺

Probably.

17 = 9 +8 9 for each squares in a row 8 for each square in a column (other than the one that is already part of the row)

Iceaka Demintika k

Le Gert Maybe the ration has to be greater than a Fibonacci-Number :)

+Le Gert That would be hilarious if they did all that work and it turned out to be an easily recognizable pattern.

+Le Gert You can only have sudokus of squares. 4, 9, 16, 25, etc.

+Jakromha 2x2 and 4x4 do equal squares. 4 and 16

Drawn808 2 won't make a sudoku, I mentioned 4.

Effortlessly

That's funny because after looking it up the puzzle has multiple solutions :)

Not all 17-clue sudokus have unique solutions, but some do. No 16-clue sudokus have unique solutions.

There are a lot of chess puzzles that a lot of math people like (for instance, try putting 8 queens on the board in such a way that none of them can capture another)

Smithy0013 put them in L shapes like the thing the knights do.

Pieter-Jan Lavaerts well spoiler alert much?

Pieter-Jan Lavaerts not enough

Chess is an excellent puzzle game. The rules are so simple that even the most plebian person can understand them, yet they're so beautifully intricate that even the most intellectuall person never will master it.

+Ann Beckman While I'm not interested in him romantically, I would love to hang out with that guy...he is interesting.

Jesse Wallis I would also love to hang out with him and just talk all about math(s) stuff. He's so passionate. I think that's what makes him super attractive to me is his passion, his intelligence and his accent among other things.

+Ann Beckman I'm impressed with the subject, too, hahaha but the guy is so English... and so skinny. I'd rather see him as a friend. may be because I'm straight.

I think I'm way more attracted to intelligence than looks (and I'm not saying others need to be like this, just saying I personally am). If someone is super intelligent and passionate I'm sold. They will then be physically attractive and turn me on by default.

thank you for explanation :-)

100 flops on a typical computer? Are you insane? The GTX Titan, which is, while being very expensive, still a consumer GPU, does 8 TeraFlops alone. Add the Prozessor to this and you'd be at 9 TFlops or so for a PC with a cost of 1500-2000 $.

I meant GFlops!! D:

That sounds a bit more realistic, albeit I would still say that it's a bit of a conservative estimate. You could probably assume an average of 3-5 TFlops oder 3000-5000 GFlops for your typical modern PC.

you could easily setup on world community grid, or ask google to run your program on their servers idle times. Both are actually easy to get done, world community grid is 100% to get done, while google wants an offer and reason for the study and who you are and such, and they do turn people down.

+SmileyMPV Interesting info. Although I find it more immpressive when viewed from the other side: You need to remove just 4 numbers to allow multiple solutions. This makes me wonder if this is the case for any grid (given you find the 4 correct numbers to remove), or if there are more 'resilient' grids that will not become ambiguous with any 4 numbers removed. I guess I should do more Sudokus...

Radonatos That is indeed quite an interesting question! So the question is: What is the highest possible amount of clues, for which there exists a sudoku grid, where given this amount of clues, it is impossible for there to be more than one valid solution?

+Enid Radaviq you're right, but i meant "What is the LOWEST amount of clues, for which there exists a grid, where given this amount of clues, it is impossible for there to be more than one solution?"

+SmileyMPV I assume it would be 78.

hehehehehe

No you can't

Mikey Whelan You can but the solution for a sudoku is not unique meaning you can get several different solutions from your starting point. (Starting with an empty grid would lead to every possible solution there is for a sudoku grid)

Mikey Whelan Yes. Called compiling:)