## Nim Square

### Problem 310

Published on Saturday, 13th November 2010, 07:00 pm; Solved by 541

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 0abc29 then the number of losing positions for the next player is 1160.

Find the number of losing positions for the next player if 0abc100 000.