Sudoku is a commonly played game where the digits 1-9 are placed in a 9x9 array.

The rules prohibit duplicate entries in rows, columns and the nine 3x3 sub-arrays.

Of course there is an astronomical number of solutions to that problem.

Now, any self-respecting Sudoku puzzle has a unique solution.

And to bring about a unique solution, some of the 81 cells come initially filled in.

One can imagine that the simplest Sudoku puzzle would have 80 cells -- all but one -- already filled in.

It would only take a glance at the 8 digits already in its row, column or 3x3 array to solve the problem.

And in general, the fewer cells that are filled in, the more difficult it is to find the unique solution.

So the question we ask is this:

If we want to make a Sudoku puzzle difficult simply by reducing the number of initially specified cells,

how many cells would have to be initially specified to still insure a unique solution?