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 $0 \le a \le b \le c \le 29$ then the number of losing positions for the next player is $1160$.
Find the number of losing positions for the next player if $0 \le a \le b \le c \le 100\,000$.
Solution
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