Martin Gardner fan John Kemeny (no relation to the Dartmouth mathematician) tells me that his niece Allison plays a kind of dice-based solitaire game ("Apparently it is all the rage at Duke, where she was, but is now spending a year at the London School of Economics" writes John) and is curious what the optimal strategy is and what the odds of winning are under optimal play. The player's goal is to knock out numbers from the set {1,2,...,12} until none remain, where the player knocks out one or two numbers on each turn as follows: the player rolls two dice, and may knock out either the sum of the two numbers or may knock out any two distinct numbers that have the same sum as the sum of the numbers shown on the dice. (Note that all that matters is the sum of the numbers the player rolls, not the numbers shown by the two dice individually.) If a player is ever in a situation where no such move is possible, the game ends. This strikes me as do-able by brute force, since there are only 2^12 states of the game (based on which numbers have been crossed out), so, starting from endgame positions and working backwards, one should be able to work out, for each position, what the optimal plays are (for each die-roll) and what the chance of winning is under optimal play. A priori, I see no reason to believe that the optimal strategy has a nice description, but then again I see no reason to believe that it doesn't! Jim Propp