Nim Square

Alice and Bob play the game Nim Square. Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number of stones from a heap. The number of stones in the three heaps is represented by the ordered triple (a,b,c). If 0≤a≤b≤c≤29 then the number of losing positions for the next player is 1160.

Find the number of losing positions for the next player if 0≤a≤b≤c≤100 000.

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter