The game:
Two players are playing a game on cube of size $100\times 100\times 100$ (Including zero). Starting the game, a coin is placed randomly on the square $\langle L,N,M\rangle$. Each player can reduce in his turn $1$ or $2$ from only one of the coordinate (and by that move the coin to the new square). The winner is the one that in his turn takes the coin to the square $\langle 0,0,0\rangle$.
The question is: if I want to be first or second, what should my strategy be (what is the invariant condition)?
What I discoverd so far:
If one of the coordinates is zero, then my invariant condition is: after each turn of mine, the distance between the other two coordinates (that are not necessarily zero) is a multiple of $3$. That is: if $\langle 0,N,M\rangle$ then the invariant condition is $|M-N|=3k$.
Edit 1: analysis of mine for several cases.
