Here's an idea for a parlor game, or contest:

The dealer (or some genius on this forum) produces an illegal puzzle, i.e. a puzzle with no solution. All givens, however, follow the rules (no two of the same digit in the same row, column, or box).

The idea is to fill in as many cells as possible, legally (i.e. without putting two of the same digit in the same row, column, or box). The player who can fill in the most cells is the winner.

For example, one player might be able to fill in 73 of the 81 cells before reaching a position where no additional cells can be filled legally. Another player, using a completely different solution, might be able to fill in 77 of the 81. The latter player is then the winner.

Another part of the contest could be to establish, somehow, the maximum and minimum number of cells that can be filled in, in the given puzzle. In the above example, 73 might be the minimum, and 77 the maximum.

Any takers?