Reference no: EM132463632

Consider the following two-person impartial combinatorial game: starting with a single pile of n chips, the players take turns at removing chips from the pile, subject to the following rule. At each move, a player is allowed to remove k chips from the pile only if k is a divisor of n, the number of chips remaining in the pile, and k < n. The player to remove the last chip wins. Compute the Sprague-Grundy function. (First try to guess it by doing some computations and then try to prove by induction.)