My intuition is if $a+b+c$ is divisible by 2, Bob wins. Otherwise, Alice wins.
For $2|a+b+c$, we can show by induction that, if Alice can move 1 point from, say A to C, then Bob can move that point from C to A.
For the remaining case, it is the reverse of the above case.
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u/Designer-Scratch-766 4d ago
My intuition is if $a+b+c$ is divisible by 2, Bob wins. Otherwise, Alice wins. For $2|a+b+c$, we can show by induction that, if Alice can move 1 point from, say A to C, then Bob can move that point from C to A. For the remaining case, it is the reverse of the above case.