## Corrupted Sudoku

Interesting puzzles can be posted here
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm

### Corrupted Sudoku

Here is a Sudoku where some of the given digits were lost in transcription. I then solved as far as possible:

Code: Select all

``````. . 5|4 . .|9 8 .
. . 7|. 1 .|3 . .
. . 3|. . .|. . .
-----+-----+-----
5 9 .|. . .|. . .
3 . .|2 . 6|. . .
. . .|. . .|. . 3
-----+-----+-----
. 5 9|. . .|4 . .
. . .|9 8 .|5 . .
. 3 1|. . 7|. . .``````
According to a reliable program, it has 3627 different solutions.

I challenge you to figure out how this puzzle has been corrupted, fix it and find the correct solution anyway.

Hint: All solved cells were singles.

Good luck, you'll need it!

Ruud
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
Para
Yokozuna
Posts: 384
Joined: Wed Nov 08, 2006 7:42 pm
Location: The Netherlands
Has anyone ever been able to figure out this puzzle?

Para
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
Digging up old memories...

It can be done.
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
Para
Yokozuna
Posts: 384
Joined: Wed Nov 08, 2006 7:42 pm
Location: The Netherlands
Maybe i misunderstood the puzzle. I thought there was some specific way this puzzle has been corrupted. For example: if two givens are a knight move from eachother, one of the two is removed(that was my first try). Now i am wondering is there a specific reason certain clues are removed or are they just "randomly" removed(for no specific reason, except for the uniqueness assumption) and that these digits are the only ones that give a unique solution.

Because what i had concluded so far, assuming a symmetrical givens pattern, was: R1C3, R2C7, R5C1 and R7C2 were the placed digits. R2C6, R3C7 and R6C8(and possibly more) were the removed givens.
But after my knight move thingy failed, i was out of ideas.

Para
Smythe Dakota
New kid on the Grid
Posts: 3
Joined: Sat Jan 12, 2008 12:14 pm
Location: Chicago
Para wrote:Has anyone ever been able to figure out this puzzle? ....
I suppose one could begin by assuming the usual newspaper symmetry among the givens. That is, if there is a given at row R column C, there is also a given at row 10-R column 10-C.

In the stated puzzle, in addition to the original givens, there would also be givens at the positions marked X below:

Code: Select all

``````. . 5|4 . .|9 8 .
. . 7|. 1 X|3 . .
. . 3|. . .|X X .
-----+-----+-----
5 9 .|. . .|. . .
3 . .|2 . 6|. . X
. . .|. . .|. X 3
-----+-----+-----
. 5 9|. . .|4 . .
. . X|9 8 .|5 . .
. 3 1|. . 7|X . .``````
Maybe that's cheating, but I couldn't help but notice the large number of symmeterically placed givens in the puzzle.

Bill Smythe
Para
Yokozuna
Posts: 384
Joined: Wed Nov 08, 2006 7:42 pm
Location: The Netherlands
Smythe Dakota wrote:
Para wrote:Has anyone ever been able to figure out this puzzle? ....
I suppose one could begin by assuming the usual newspaper symmetry among the givens. That is, if there is a given at row R column C, there is also a given at row 10-R column 10-C.

In the stated puzzle, in addition to the original givens, there would also be givens at the positions marked X below:

Code: Select all

``````. . 5|4 . .|9 8 .
. . 7|. 1 X|3 . .
. . 3|. . .|X X .
-----+-----+-----
5 9 .|. . .|. . .
3 . .|2 . 6|. . X
. . .|. . .|. X 3
-----+-----+-----
. 5 9|. . .|4 . .
. . X|9 8 .|5 . .
. 3 1|. . 7|X . .``````
Maybe that's cheating, but I couldn't help but notice the large number of symmeterically placed givens in the puzzle.

Bill Smythe
Actually i think there are less givens, because as Ruud stated a few singles were already filled. So i have a feeling this is the original puzzles format. Otherwise it would be too many givens to figure out. I think this is enough to make it unique. 3 givens is enough to work with.

Code: Select all

``````. . .|4 . .|9 8 .
. . 7|. 1 X|. . .
. . 3|. . .|X . .
-----+-----+-----
5 9 .|. . .|. . .
. . .|2 . 6|. . .
. . .|. . .|. X 3
-----+-----+-----
. . 9|. . .|4 . .
. . .|9 8 .|5 . .
. 3 1|. . 7|. . .``````
Filling only singles here without the X's gives you the grid given by Ruud

My problem with this puzzle is that it seems to be completely random why a number has been deleted. At least i can't find a logical process which explains which number has been deleted. The only rule behind the puzzle is probably that only one combination of 3 numbers guarantees a unique solution. Then it is not really a fun puzzle as proving uniqueness by hand for each number combination is a completely annoying. So this really seems to be a programmers puzzle. That is why i have given up on it. Maybe there is some logical process behind it, but i can't detect it at least.

The link that Ruud gave was also based on uniqueness, which is no fun by hand.