"Say Andy takes 6, 7, 8, 9 or 10 cookies. He will end up having the most cookies, which fails condition 1. So he doesn't do that. Say Andy takes 5 cookies. Bea will take 4, which means she will end in the middle and Andy still fails condition 1. So he doesnt do that either. Say Andy takes 4 pieces. Bea cannot fulfil condition 1. (If Bea takes, 1, 2 or 3, then Celine takes 4 and Celine wins."
"If Bea takes 4 or more she will have the most, or joint most, cookies.) So, Bea realises her best outcome is to fulfil condition 2. She takes all the remaining cookies, and Celine is left with 0. If Andy wins by taking 4 pieces, he is not going to take any less pieces since that falls foul of condition 2. He wants both to be middle, and to have as many cookies as possible. So he takes 4 pieces."
Andy, Bea, and Celine alternate taking cookies from a jar of ten, with Andy first, Bea second, Celine third. Each prefers not to finish with the most or the least cookies, and otherwise prefers more cookies. Andy reasons that taking 6–10 would give him the most, and taking 5 allows Bea to take 4 and still leave Andy with the most. By taking 4, Andy forces a situation where Bea cannot avoid being most or least except by maximising, so Bea takes the remaining 6 and Celine is left with 0.
Read at www.theguardian.com
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