I posed the following problem to some of my (former?) friends: play a legal chess game, and reach a "double stalemate" position where neither side has any legal moves. Among all such games, find the one involving the fewest captures, and among all those, the shortest game. Monty McGovern produced a solution involving only 1 capture by each side. If no solutions with (0,1) or (0,0) captures exist, that would mean McGovern's solution is optimal in that sense. Optimization of the length of the game is a worse kettle of fish... -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)