Exotics at World Sudoku Championships

Agent Allen

There was an article in the London Times on Monday 6th March 2006 about the inaugural world championships in Lucca, Italy.
In the article several variants were mentioned, though two are a special case of more general rule. They weren't named so I'll use the name I know:
There's nonomino Sudoku (non-square sub-grids).
Sudoku Cross (where the main diagonals need to contain 1-9 along with the standard constraints)
And another variant I don't know the name of (anyone?).
That is where there is a constraint over which numbers can go in certain cells.
So for example some cells are grey and they're for even numbers and some cells are white for odd.
A similar variant marks circles for 1,2 and 3, squares for 4,5,6 and 'empty' for 7,8,9.
The last two are special cases of some sort of sub-set constraint.
I notice this in fact partitions the puzzle in to a set of independent sub-puzzles where placing the one set provides no new information about the other sets.

The article also mentions sum and product constraints. The times calls sum constraints 'Killer Su doku'(sic).
I've never seen a product constraint puzzle. Sounds like fun for anyone who knows the fundamental theorem of arithmetic!

It got me thinking that:
1. Do we need/have a proper catalogue of variants?
2. How about a crazy framework where we can cook up all manner of beasts?
Mix and match constraints! Nonominio Cross Sudoku with odds and evens shaded with a few sum and product constraints thrown in for a laugh.
Then write a routine that gives birth to some real horrors.
Remember to chuck in a rule it checks that the puzzle is not soluble without using all the classes of constraint or even all the constraints.
Alternatively it might knock out constraints until the puzzle is ambiguous and then put the last one back.
We could even pile in a crazy constraint like 'these four blue cells contain the numbers 1,2 & 3 along with another unspecified number!
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Agent A

nero · Posted: Mon Apr 03, 2006 9:04 pm Post subject:

I already have a nonomino-style puzzle generator. It's written in Java, and based on a C version that I wrote a few years back. Technically, it does more than nonominoes, since it can generate grids of size other than 9 (I created one that I call 10x10 square-ish, which contains mostly 3x3 regions with an extra square sticking out the side).

You can see it at http://www.employees.org/~numplace.

On a side note, there are some interesting properties about non-rectangular puzzles that I've taken advantage of in the generator algorithm. Try a few 10x10 square-ish puzzles, and note that certain squares are "linked", in that one always has the same number as the other.