5 puzzles differing in one number in the same cell

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5 puzzles differing in one number in the same cell

Postby maria45 » Sun Aug 20, 2006 7:27 pm

Hello you programmers,

just played around a bit with sudoku explainer, and I came upon some puzzles which differ only in one number in the same cell:

5..7...1..6..4...7..3..24....48..2...1..3..8.2....9..4..86..3...3..2..5.9....5..6
5..7...1..6..4...7..3..25....48..2...1..3..8.2....9..4..86..3...3..2..5.9....5..6
5..7...1..6..4...7..3..26....48..2...1..3..8.2....9..4..86..3...3..2..5.9....5..6
5..7...1..6..4...7..3..28....48..2...1..3..8.2....9..4..86..3...3..2..5.9....5..6
5..7...1..6..4...7..3..29....48..2...1..3..8.2....9..4..86..3...3..2..5.9....5..6

Despite the complicatedly looking pattern with many diagonal givens, all five puzzles solve with singles.

I wonder wether there are other puzzles like this, differing in only one given in the same cell and how many different puzzle are possible with this variation, and if there could exist a puzzle with all nine possible values in a cell, each resulting in a valid (i.e. with unique solution) sudoku.
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Re: 5 puzzles differing in one number in the same cell

Postby JPF » Sun Aug 20, 2006 7:51 pm

maria45 wrote:I wonder wether there are other puzzles like this, differing in only one given in the same cell and how many different puzzle are possible with this variation, and if there could exist a puzzle with all nine possible values in a cell, each resulting in a valid (i.e. with unique solution) sudoku.


I posted this one, 2 months ago :

Code: Select all
[3,4,5,8,9 are valid digits in A = r4c9]

 . . . | 2 . 8 | 1 . .
 . 4 3 | . . . | . 8 .
 . 9 . | . . . | . 5 .
-------+-------+-------
 1 . . | . . 6 | 7 . 9
 . . . | 5 . . | 2 6 .
 6 . . | . 2 . | . . .
-------+-------+-------
 . 7 . | . . . | . . .
 . . . | . 6 . | 9 . .
 . . 8 | 9 . 5 | . . 1


So far, my personal record is 5 .
[Edit : wording]

JPF
Last edited by JPF on Sun Aug 20, 2006 6:56 pm, edited 1 time in total.
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Postby ravel » Sun Aug 20, 2006 8:18 pm

Puzzles with 2 possible givens in the same cell were called twins by gfroyle. I have tried some (harder ones) and noticed that the solution paths were very similar.
But this is not the case for JPF's puzzles. The puzzle with 3 needs a chain, with 9 it is singles only.
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Postby JPF » Sun Aug 20, 2006 9:08 pm

one other example :

Code: Select all
r3c9 = [1,2,5,6,9]

 9 . . | 1 . . | . 7 .
 . . 6 | . 4 . | . 8 3
 . . . | . . . | . . 5
-------+-------+-------
 . 7 . | 5 . . | . . .
 . . . | . . 3 | . . .
 . . . | 9 . . | . 5 4
-------+-------+-------
 . 1 5 | . . 2 | 3 4 .
 . . 3 | 7 5 . | 2 . .
 . 8 . | 6 . . | . . .



JPF
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