Wednesday, December 17, 2008

Ambiguous Sudoku

Today's San Jose Mercury News (print edition) has an ambiguous Sudoku:
2-8--3--9
----8-4-5
-6------7
--12-----
-9-4-1---
-----98--
9------4-
5-2-4-1--
6--3--9-2
The solution can have 5 or 7 in each of the entries in Rows 1 and 6, Columns 4 and 5.

Real Sudokus are supposed to have unique solutions. Sometimes the uniqueness is useful in finding a solution.

Update: As a comment below shows, I was wrong about this. The solution is unique as it is supposed to be.

Unknown said...

I found only one solution:

2 4 8 5 7 3 6 1 9
1 7 9 6 8 2 4 3 5
3 6 5 1 9 4 2 8 7
7 5 1 2 6 8 3 9 4
8 9 3 4 5 1 7 2 6
4 2 6 7 3 9 8 5 1
9 1 7 8 2 6 5 4 3
5 3 2 9 4 7 1 6 8
6 8 4 3 1 5 9 7 2

What is the second?

Roger said...

Now I am puzzled, and I no longer have my solution. You solution does not have the ambiguity that I described. But it does have another ambiguity.

To explain the ambiguity that I was claiming, look at the "2 4" at the start of the first row in your solution, and the "4 2" at the start of the sixth. You could reverse the 2 and 4 in both cases, and the sodoku would have all the same properties. If yours is a solution, then flipping these two pairs of digits would give another solution.

In this case, flipping the digits would not be consistent with the original pattern. I'll have to look at this some more.

Unknown said...

But 2 in top left corner is fixed

Roger said...

Okay, you are correct. I just redid the sudoku from scratch, and I get the same answer as yours as the unique solution. I don't know how I got this wrong. I did determine the 5s and 7s at the end, so perhaps I got sloppy with the 5s and 7s as I was finishing. Anyway, thanks for pointing out my error!