sudoku break

While in Warwick last week, one evening after having exhausted my laptop battery, I tried the following Sudoku (from Libération):

>   printSudoku(readSudoku("libe.dk"))
  +-------+-------+-------+
  | 4   6 |   2   | 3   9 |
  |   3   |       |   2   |
  | 7   2 |       | 5   6 |
  +-------+-------+-------+
  |       | 9 4 5 |       |
  | 5     | 7 6 2 |     1 |
  |       | 3 1 8 |       |
  +-------+-------+-------+
  | 6   9 |       | 1   3 |
  |   7   |       |   9   |
  | 3   1 |   9   | 4   7 |
  +-------+-------+-------+

and could not even start. As it happened, this was a setting with no deterministic move, i.e. all free/empty entries had multiple possible values. So after trying for a while and following trees to no obvious contradiction (!) I decided to give up and on the next day (with power) to call my “old” sudoku solver (built while at SAMSI), using simulated annealing and got the result after a few thousand iterations. The detail of the exploration is represented above, the two colours being code for two different moves on the Sudoku table. Leading to the solution

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

I then tried a variant with more proposals (hence more colours) at each iteration, which ended up being stuck at a penalty of 4 (instead of 0) in the final thousand iterations. Although this is a one occurrence experiment, I find it interesting that having move proposals may get the algorithm stuck faster in a local minimum. Nothing very deep there, of course..!