Diabolical Sudokus

Diabolical Sudokus

When is a Sudoku diabolical?

When it can't be solved by a human being (without the aid of a computer program) by any means except dumb luck.

We want to look at one of these infernal puzzles to get some idea of what they're like.

 

Vidar's Monster #3

Vidar put out some other monstrous Sudokus, but this particular one has been widely circulated on the Web as an example of a Diabolical Sudoku.

It looks like this:

Vidar's Monster #3 24 Clues — not a lot, but the number of Clues is not a reliable indicator of difficulty. We need to see what the inner structure looks like.

And what shows us the inner structure?  Putting in the Candie Markup and the Twin Tagging:

Vidar's Monster #3, marked up & Twin-tagged. (Ignore the one coloured Cell.) Two Locked Sets gave us two more BigNums (a 5 and an 8). There were no Claims. Two 2-Fish killed a few 5- and 8-candies. Stuck. No more moves. One for the shredder.

Well, before shredding it, I worked up some hocus-pocus theories and selected about a dozen Trio or Quartet Cells from which to spring a three-way or a four-way Fork.

That really wasn't too bright. I generated many, many Stalemates (a series of moves that stops dead before yielding either a Solution or a Conflict).

And then I tried setting the yellow Cell equal to 2. After some Locked Sets, some Claims, a 2-Fish, and a miserable minimal-result UR, I actually reached a Solution!

Uh-huh.

What I had found was a proverbial Back Door — one magic Cell that, if you pick it right, leads you to a Solution.

And the logic behind that?  Zilch, of course.

That's why Forks have such a bad reputation in the Sudoku world. If you fork with no strong rationale, then you'll generate a mess of Stalemates, and if you do eventually find a Solution, it's just a matter of luck.

Needless to say, I maintain that a Smart Fork is a different proposition. But if you look at this Grid, you won't find anything that comes even close to being a high-Twin-link-Degree Fault Point from which to launch a Smart Fork.

What's wrong with this Grid? Two things:

• Not enough Pair Cells. (There are three.)

• Not enough Twins, and not enough linkage between them.

The shortage of Twins means that we're not going to find a long Tightly Linked Twin Chain that constitutes a Worthy Target.  There is a 6-Cell Twin Chain in 5 and a 6-Cell Twin Chain in 8, but they're not tightly linked to each other. The other Twin Chains are smaller. So there's no hope for finding a decent Target Chain.  And beyond that, the shortage of both Pairs and Twins means that it would be hard to construct an Attack Chain even if we had a Worthy Target.

Those are the physical characteristics of a Diabolical Sudoku.

You can't solve it by hand, unless you want to shoot a lot of time trying things at random — and that doesn't generate much satisfaction.

Is this the hardest Sudoku?

No. There are many other known Diabolical Sudokus, and some of them don't even have a Back Door. Check the Links page, near the end, for a few sites that provide more of these for the benefit of the masochists who need to feel more pain.

Is there any hope?

Hope springs eternal. See The Quest for some remarks on the Holy Grail aspect.