# Schizo: a different sudoku solving technique

Over the years, several tips and techniques have been developed to help solve sudoku puzzles with logic rather than brute force. To name a few, sudoku9x9 mentions (among others) hidden single, naked single, x-wing.

## At least one solution

These techniques are all based on a common principle: they work « ad absurdum », by eliminating moves that would lead to an invalid grid: a puzzle with zero solution. For example, the grid below illustrates the hidden single technique:

 2 1 3 2

Number 2 cannot be placed in any of the red cells because this would lead to a grid with no solution. Therefore it must be placed in the green cell, leading to the next step:

 2 1 2 3 2

## At most one solution

Here is a (novel?) technique based on the opposite principle: it works by eliminating a move that would lead to a grid with more than one solution. (By current rules, well formed sudoku puzzles must have a single solution.)

[ EDIT — This technique is in fact well known to people such as the folks at cracking the cryptic. ]

The grid below illustrates this technique, which we call schizo (as in schizophrenia):

 3 6 1 2 2 5 1 48 478 9 3 6 6 3 2 478 5 1 9 2 48 48 7 1 7 1 9 5 3 6 2 8 4 1 9 2 4 2 7 1 3 5 1 9 5 8 2 5 6 2 4 1

Number 7 cannot be placed in the red cell because this would eventually lead to two equally valid solutions:

 3 6 1 2 2 5 1 4 8 9 3 6 6 3 2 7 5 1 9 2 8 4 7 1 7 1 9 5 3 6 2 8 4 1 9 2 4 2 7 1 3 5 1 9 5 8 2 5 6 2 4 1
 3 6 1 2 2 5 1 8 4 9 3 6 6 3 2 7 5 1 9 2 4 8 7 1 7 1 9 5 3 6 2 8 4 1 9 2 4 2 7 1 3 5 1 9 5 8 2 5 6 2 4 1

Therefore 7 must be placed in the green cell, leading to the next step:

 3 6 1 2 2 5 1 48 7 9 3 6 6 3 2 48 5 1 9 2 48 48 7 1 7 1 9 5 3 6 2 8 4 1 9 2 4 2 7 1 3 5 1 9 5 8 2 5 6 2 4 1

$\Box$

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