Logic puzzle solution: Andy 4, Bea 6, Celine 0

Earlier today the setter of a logic puzzle posted as a pre-commemoration of World Logic Day (January 14) published the solution: with the priority that avoiding being the sole or joint most or least is more important than maximising cookies, Andy takes 4, Bea takes 6 and Celine ends with 0.

The puzzle begins with a jar of ten cookies and players Andy, Bea and Celine taking turns (Andy first, then Bea, then Celine). On each turn a player may take as many cookies as they like. They agree on two conditions: (1) no one wants to finish with the most or the least (including joint most or joint least), and (2) they want as many cookies as possible.

Condition 1 has priority over condition 2. The friends cannot communicate, may take nothing, and are assumed to act rationally and in their best interests. The setter’s reasoning rejects Andy taking 6–10 (he would have the most) or 5 (Bea would then take 4 and Andy still fails condition 1).

If Andy takes 4, Bea cannot fulfil condition 1 and so, prioritising condition 2, takes all remaining cookies, leaving Celine with none. The setter adds that Andy would not take fewer than 4 because that would violate condition 2, so Andy takes 4. The puzzle post ends by noting the setter will be back in two weeks and thanks Deniz Sarikaya of World Logic Day for the contribution.

Key Topics

Science, Logic Puzzle, World Logic Day, Andy, Bea, Celine