## 5 puzzles differing in one number in the same cell

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

### 5 puzzles differing in one number in the same cell

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.
maria45

Posts: 54
Joined: 23 October 2005

### Re: 5 puzzles differing in one number in the same cell

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.
JPF
2017 Supporter

Posts: 3752
Joined: 06 December 2005
Location: Paris, France

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.
ravel

Posts: 998
Joined: 21 February 2006

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
JPF
2017 Supporter

Posts: 3752
Joined: 06 December 2005
Location: Paris, France