Problem 310Published on Saturday, 13th November 2010, 07:00 pm; Solved by 599; Difficulty rating: 40%
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.