Take Away a Perfect Square
A pile contains n stones. Two players alternate; on each turn a player must remove a positive perfect square number of stones (1, 4, 9, 16, ...), no more than the pile holds. The player who takes the last stone wins. For how many values of n with 1 ≤ n ≤ 100 does the player to move lose with optimal play? Give an integer.
Related problems
Source: Classic take-away game (squares); no traceable original source. Statement written for AxiomIQ.