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

2 posts
• Page **1** of **1**

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

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.

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...

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

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