The World's Hardest Sudoku (June 2012)

**SKG_Scintill** · 07-12-2012, 05:11 PM

Re: The World's Hardest Sudoku (June 2012)

**Reincarnate** · 07-12-2012, 05:15 PM

Re: The World's Hardest Sudoku (June 2012)

Yikes, that one is messy

**Reincarnate** · 07-12-2012, 05:43 PM

Re: The World's Hardest Sudoku (June 2012)

Oh, right, the explanation:

Normally you can seed each square with a subgrid containing all values 1-9 (indicating possible values) and then eliminate all those that are impossible. For easier puzzles this makes it clear which squares to fill in. When you do this for this puzzle, you find that none of the currently unknown-squares have one tick left. At this point, you typically invoke recursive techniques and what have you, which are trivial for computers to solve but not realistically feasible for humans.

However, it's worth noting that the square in position (7,2) (the middle-row left-column square within the lower right primary square) only has two possible values: 9 and 3. None of the other unknowns have so few potentials, so that's a good place to begin a guess-and-check method.

**Herogashix** · 07-12-2012, 05:47 PM

Re: The World's Hardest Sudoku (June 2012)

Okay Rubix.

**Reincarnate** · 07-12-2012, 05:52 PM

Re: The World's Hardest Sudoku (June 2012)

You disagree?

**iironiic** · 07-12-2012, 07:08 PM

Re: The World's Hardest Sudoku (June 2012)

Originally posted by Reincarnate

Oh, right, the explanation:

Normally you can seed each square with a subgrid containing all values 1-9 (indicating possible values) and then eliminate all those that are impossible. For easier puzzles this makes it clear which squares to fill in. When you do this for this puzzle, you find that none of the currently unknown-squares have one tick left. At this point, you typically invoke recursive techniques and what have you, which are trivial for computers to solve but not realistically feasible for humans.

However, it's worth noting that the square in position (7,2) (the middle-row left-column square within the lower right primary square) only has two possible values: 9 and 3. None of the other unknowns have so few potentials, so that's a good place to begin a guess-and-check method.

Although I agree with this, I'm sure there is a logical way to tackle all Sudoku puzzles. At least, from what I have been told, Sudoku challenges you to figure out the placement of numbers using pure logic. I suppose brute forcing your way through by guess and checking works, but it's more interesting to figure out a concrete logical way to place all of the numbers in their appropriate spots.

**Izzy** · 07-12-2012, 07:57 PM

Re: The World's Hardest Sudoku (June 2012)

Originally posted by SKG_Scintill

Not solvable. You already used up all the values you have.

**dag12** · 07-12-2012, 08:13 PM

Re: The World's Hardest Sudoku (June 2012)

are we guaranteed that there exists only one unique solution? If not, it would explain why it's easy to solve via guess and check, but hard to solve via logic.

**TheSaxRunner05** · 07-12-2012, 09:01 PM

Re: The World's Hardest Sudoku (June 2012)

I would only be able to solve this by the guess and check method, and it's still questionable for me at that.

**dag12** · 07-12-2012, 09:14 PM

Re: The World's Hardest Sudoku (June 2012)

Nevermind, got my first number.
Edit: And solved by hand.

**Reincarnate** · 07-12-2012, 10:24 PM

Re: The World's Hardest Sudoku (June 2012)

Originally posted by iironiic

Although I agree with this, I'm sure there is a logical way to tackle all Sudoku puzzles. At least, from what I have been told, Sudoku challenges you to figure out the placement of numbers using pure logic. I suppose brute forcing your way through by guess and checking works, but it's more interesting to figure out a concrete logical way to place all of the numbers in their appropriate spots.

I wrote a Sudoku solver a long while back. You can indeed solve them through logic alone, but it usually involves deeper searches that humans aren't really up for performing.

What makes this puzzle "hard" is actually more a form of tedium. You have to plan ahead a few levels of depth since you don't wind up with single-ticked boxes after eliminating all the collisions. I solved it by hand by making a few educated guesses early on (and then the rest just kinda fell into place). I didn't solve it via braindead algorithm because it seemed like there were going to be too many instances where I'd be faced with two or more choices, which multiply out pretty quickly. But it's also possible that these dual-pronged dilemmas only last for a couple rounds -- I didn't check. Would have to ask dag what his approach was.

dag: As far as I can tell, there's only one unique solution.

**dag12** · 07-12-2012, 10:29 PM

Re: The World's Hardest Sudoku (June 2012)

As far as I know, there isn't a clean logical way to do it.
My method used a brute force proof by contradiction haha (though for many places where there are two possible choices, it's hard even to just find a contradiction for one of them)

Originally posted by Reincarnate

I wrote a Sudoku solver a long while back. You can indeed solve them through logic alone, but it usually involves deeper searches that humans aren't really up for performing.

What makes this puzzle "hard" is actually more a form of tedium. You have to plan ahead a few levels of depth since you don't wind up with single-ticked boxes after eliminating all the collisions. I solved it by hand by making a few educated guesses early on (and then the rest just kinda fell into place). I didn't solve it via braindead algorithm because it seemed like there were going to be too many instances where I'd be faced with two or more choices, which multiply out pretty quickly. But it's also possible that these dual-pronged dilemmas only last for a couple rounds -- I didn't check. Would have to ask dag what his approach was.

**Reincarnate** · 07-12-2012, 10:34 PM

Re: The World's Hardest Sudoku (June 2012)

On second thought I think you're right -- by "logic alone" I mean to imply that they can be algorithmically solved for even if collision-removals aren't sufficient. Of course, with sufficient depth, that algorithm becomes indistinguishable from brute force, which may not feel as "logical."

**dag12** · 07-12-2012, 10:43 PM

Re: The World's Hardest Sudoku (June 2012)

If there's only one unique solution, you could technically 'logically' disprove every other alternative to get to the solution. By definition, that's still logic.

Though of course, whether that intuitively feels logical is another matter.

The World's Hardest Sudoku (June 2012)

The World's Hardest Sudoku (June 2012)

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