The Tower of Hanoi game is a classical puzzle in recreational mathematics
(Lucas 1883) which also has a strong record in pure mathematics. In a borderland
between these two areas we find the characterization of the minimal number of moves,
which is 2n −1, to transfer a tower of n disks. But there are also other variations to the
game, involving for example real number weights on the moves of the disks. This gives
rise to a similar type of problem, but where the final score seeks to be optimized. We
study extensions of the one-player setting to two players, invoking classical winning
conditions in combinatorial game theory such as the player who moves last wins, or
the highest score wins. Here we solve both these winning conditions on three p

• Two-player Tower of Hanoi