Repeated Numbers

[jonluntzel]

When I enter an input such as 1 1 1 2 2 2 3 3 0 with an end state of 3 3 2 2 2 1 1 1 0, the program is not solving for a particular ordering of the 3's tiles, 2's, and 1's, but rather finds any solution that matches the end state, correct? Likewise, is it acceptable to use multiple 0's to indicate there is more than one empty space that can be allocated?

[jonluntzel]

For anybody else interested it seems that it is not solving for a particular ordering when the board has repeated tiles, but does not allow multiple empty spaces.