## Multiply Solution

Everything about Sudoku that doesn't fit in one of the other sections

### Multiply Solution

Hi,

Is there methods to detect multi solutions grids without solve them
two times?
Befoe to search I don't want to 'reinventing the wheel'!
Pay
Papy

Posts: 131
Joined: 15 August 2006

Hi,

Lik I Have no answer I study the multiply solutions grids

In fact youhave two reasons to have multiplky soluces:
1- The dispositiooons of the digit on the latin square
2- The repartition of the values in the clues.

At this time I only stuidy the first point:

The result is: like on valids grids you have Intouchables squares
Deecting them , or using them, make the positions of the clues more easy
To illustrate here is a sample with a block.

R1 1 2 3 4 5 6 7 8 9
R2 7 9 6 1 8 x x x 5
R3 x x x x x x 6 x x

Look at r1c3 r2c3 and r1c6 r2c6 we have a paire 36ans aan other 6x
in r2c6 we can put the 2 or 3
If we choosethe 3 ve obtain the paires 36 and 63 . It"s wrong!
why? Because we cxan inverse 36 36 in 63 36 and the soluice will be ood
So here ius one of the mechanism of the multisolutions grid
A rectangle with 2x2 identicals digits.
But it's strange inb many valids grids we found rectanles?
Yes it's true but loojk well one corner (ore more) are a clue!
Fixing the value by a clue make impoissible the permutation and the disposition is good.

French Paires
if you have a rect with 3 corners set (with two with the same value) the missing cornar cannot have the same value than his oppoed. It's treue ifo corner is a clue.

Is't easy when makingl atin square to select those without pairs: I call tem the Intouchables squares.

Papy
For the second point I search...
Papy

Posts: 131
Joined: 15 August 2006