# Sudoku lovers, uniteNovember 7, 2013 7:22 PM   Subscribe

I like to think I'm fairly good at Sudoku, but this one has me stumped. I know the interwebs is replete with automatic solvers, but I want to be able to solve this by myself. Even just the first step (!) and the thought logic behind it would be greatly appreciated. Thank you, MeFi!
posted by bigasthesky to Sports, Hobbies, & Recreation (8 answers total) 4 users marked this as a favorite

posted by Jacen at 7:29 PM on November 7, 2013

I don't think there's enough information to solve it, right? If there's not at least one 2 or one 3 on the grid, there's at least two possible solutions.
posted by Jeanne at 7:31 PM on November 7, 2013 [2 favorites]

FWIW I plugged it into an online solver which said there wasn't enough information to solve it. This doesn't mean there isn't a solution, just that it isn't unique.
posted by dilaudid at 7:36 PM on November 7, 2013

Best answer: I also plugged it into an online solver and it said there wasn't enough information. I threw a 2 and a 3 in randomly and it gave me a solution. I put them in different places and it gave me a different solution. This is good news -- it means you are actually fairly good at Sudoku (or at least not definitely bad)!

The problem is that this wasn't Sudoku, it was a group of random numbers nefariously placed in a grid to ensnare people who like puzzles.
posted by Mrs. Pterodactyl at 7:43 PM on November 7, 2013 [4 favorites]

I guess see if tomorrow they print an answer or do they print an apology for a typo.
posted by RobotHero at 7:44 PM on November 7, 2013 [1 favorite]

Best answer: There are only 14 clues. The minimum number of clues required to uniquely solve a Sudoku is 17.

Maybe you can take a page from CPUs that do speculative execution: sometimes, you can just make a few mutually-exclusive guesses in parallel and stop developing the consequences of a guess when it becomes clear that the guess is incorrect.

To start this process, look at some numbers (or squares) that are almost but not quite determined. For example, in the top middle square, there are two places a 4 can go. In the middle square, there are two places an 8 can go. In the lower left square, there are two places a 5 can go. Etc. Make several copies of the puzzle and start guessing and seeing which guesses force you into an inconsistency.

You may wish to start by evaluating guesses optimistically- if you guess right, then you're progressing towards a solution faster, and if you guess wrong, optimistic guessing will reach a contradiction faster. For example, in the top middle square, you have two choices for where to put the four. But one of those choices (the bottom right) narrows the possible places for the top middle square's 5 to two (top right or middle right). Explore that first. Etc.
posted by a snickering nuthatch at 8:55 PM on November 7, 2013 [2 favorites]

Best answer: As Jpfed says 17 is the minimum number of "givens" for a Sudoku to be uniquely solvable, and unique solvability is usually the definition of a "valid" Sudoku.

This one has in excess of 1,000,000 solutions according to my little recursive C Sudoku solutions counter (part of a project that's on hold). I tried to get the "real" count but started running out of RAM, I suspect it has billions of solutions.

So that's either the mother of all typos or someone is pulling your leg.
posted by hardcode at 2:01 AM on November 8, 2013 [1 favorite]

Response by poster: Thank you for all the great answers! I just learned something new today -- which is that a valid Sudoku puzzle should have at least 17 givens. Unfortunately, I have no way of checking if this was just indeed a typo because the puzzle was given to me as a photocopy by my mom, who got it from my uncle, who couldn't solve it either.
posted by bigasthesky at 2:06 AM on November 8, 2013

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