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Saturday, December 10, 2005

Sudoku Math and Strategies

For those of you who are still addicted to Sudoku, here are explanations of two strategies for solving them (courtesy of CMT):

The X-Wing:
X-Wings are fairly easy to spot, but a little harder to understand than some other techniques. Like others it relies on using positions of pencilmarks to infer enough to allow you to eliminate some other candidates.

X-Wings are when there are two lines, each having the same two positions for a number.
The Swordfish:

This is very similar to using X-Wings, in that it will allow you to use knowledge about rows to remove candidates from columns, and vice versa. Make sure you're happy with why X-Wings work before moving on to Swordfish!

The complexity here is that you're using knowledge from 3 rows at the same time - and that's what makes them harder to spot. Unlike X-Wings, they don't form a simple rectangle.

If you're really intrigued by the mathematics (and a bit of history) behind Sudoku, check out this article [h/t to Tyler Cowen]:
From a computational point of view, Sudoku is a constraint-satisfaction problem. The constraints are the rules forbidding two cells in the same neighborhood to have the same value; a solution is an assignment of values to cells that satisfies all the constraints simultaneously.
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