I suspect that among the readers of this column, few are unfamiliar with Sudoku. The same cannot be said about Sudokill, a game invented for a graduate class I teach. Sukokill is a two-person game in which players try to force each other to violate the Sudoku rules.

Here's a quick refresher on Sudoku. The goal is to fill a nine-by-nine grid with digits between 1 and 9. Each digit should appear exactly once in each row, once in each column and once in each nonoverlapping three-by-three box starting from the upper left corner.

In the following example, we use 0 to represent a blank.

0 0 0 0 0 0 0 0 7 7 0 4 0 0 0 8 9 3 0 0 6 8 0 2 0 0 0 0 0 7 5 2 8 6 0 0 0 8 0 0 0 6 7 0 1 9 0 3 4 0 0 0 8 0 0 0 0 7 0 4 9 0 0 6 0 0 0 9 0 0 0 0 4 5 9 0 0 0 1 0 8

Consider the lower left box:

0 0 0             7 0 4             0 0 6             0 0 7             0 8 0             9 0 3             0 0 0 7 0 4 9 0 0 6 0 0 0 9 0 0 0 0 4 5 9 0 0 0 1 0

8

We know that of the five blanks in the lower left box, one must be 7. Because there is a 7 in the third column and also a 7 in the seventh (from the top) row, the only legal place for a 7 is to the right of the 6, yielding:

0 0 0             7 0 4             0 0 6             0 0 7             0 8 0             9 0 3             0 0 0 7 0 4 9 0 0 6 7 0 0 9 0 0 0 0 4 5 9 0 0 0 1 0

8

By contrast, the following would be illegal:

0 0 0             7 0 4             0 0 6             0 0 7             0 8 0             9 0 3             0 7 0 7 0 4 9 0 0 6 0 0 0 9 0 0 0 0 4 5 9 0 0 0 1 0

8

... because then there would be two 7s in the same row.