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A puzzle that asks for determining the winner in a multi-player game.

10
votes
Let $a,b,c$ be the numbers at the corners and $d,e,f$ be the numbers at the midpoints (say $d$ opposite $a$, $e$ opposite $b$, $f$ opposite $c$). To fix the rotation and reflection of a given solution …
answered May 26 '15 by Rand al'Thor
10
votes
Alice wins if and only if Proof By induction. Firstly, $n=2$ is obviously a winning position, while $n=3$ is a losing position because the only allowed move is to remove one pebble, leaving the wi …
answered May 25 '15 by Rand al'Thor
14
votes
Solution Step-by-step deduction If A plays first, then Proof: the crucial realisation is that B can always force A to play in a specific square. WLOG, say A's first move is an $X$. If A's f …
answered Feb 18 '17 by Rand al'Thor
5
votes
The key fact is as follows: Therefore this particular game ends when the numbers on the board are So the conclusion is …
answered Mar 30 '19 by Rand al'Thor
1
vote
If it gets to the stage when there's only 1 coin left, then it's B turn to make an offer, so If it gets to the stage when there are 2 coins left, then it's A's turn, but because of the above, If …
answered Dec 2 '16 by Rand al'Thor
57
votes
It doesn't matter which option you choose, because Your probability of survival if you're one of n players left is as follows: Informal proof It was established in the question that if there ar …
answered Dec 28 '14 by Rand al'Thor