The New Sudoku Players' Forum

[qqwref]

There have been a lot of topics here where someone has found an amazing puzzle (or a few) that has a specific, rare characteristic. An example is dusoku's puzzle that has two solutions, which differ in 44 cells:

Code: Select all

1.. ... 58.
8.. ..1 ..6
.6. .2. ...

... 59. ...
... .7. ...
.93 ..2 ...

.1. ... 8.4
... 9.7 .5.
6.. 2.. 71.

So I was thinking that we could put together all of the puzzles that have been found to have a special characteristic. If you know of or have constructed a puzzle with a specific characteristic, post or discuss it here! Remember to say who made a puzzle you post, even if it was you. I think it would be interesting to put together all of these amazing puzzles in a gallery of sorts; it would be really too bad if any of these mathematically interesting Sudokus would be lost just because nobody has posted in a topic for too long!

[Pat]

re: exactly 2 answers


2 answers - lowest number of clues:

There are quite a few "near misses" that I have found..

Code: Select all

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



is interesting, because it has only 16 clues. It CANNOT be uniquely solvable, because it is missing both 8 and 9, and so they can always be exchanged in any final solution.

But, this turns out to be the only problem - the puzzle has exactly TWO solutions...

2 answers - greatest divergence possible?

[ 24 clues ]

2 answers differ in 48 cells:

Code: Select all

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



[ update: ] Red Ed has now done better - 2 answers differ in 55 cells:

The biggest minimal unavoidables:
55 2
{11,13,15,16,18,19,21,22,24,26,27,29,31,32,33,34,35,36,37,38,43,44,46,49,52,53,54,55,56,58,61,64,65,67,68,69,72,75,76,77,79,81,82,83,84,85,88,89,91,92,93,95,96,98,99}

Here is the "ambiguity that involves 9 digits and 55 cells":

Code: Select all

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



[ update: ] JPF has now done better - 2 answers differ in 58 cells:

21 clues

Code: Select all

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



[ update: ] Ocean has now done better - 2 answers differ in 60 cells:

21 clues

Code: Select all

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