In a fascinating exercise of logic and game theory, a puzzle set to commemorate the upcoming World Logic Day has revealed a counter-intuitive solution for three friends dividing a jar of cookies. The scenario, which pits Andy, Bea, and Celine against each other under strict rational conditions, concludes with a decidedly uneven distribution.
The Puzzle Parameters: Greed, Shame, and Rationality
The friends, who are not permitted to communicate or form alliances, have a jar containing ten cookies. They take turns, starting with Andy, then Bea, then Celine. On each turn, they may take as many cookies as they wish, and they are not obliged to take all ten.
They operate under two key conditions, with the first taking absolute priority. Condition one states that no one wants to finish with the most or the fewest cookies, as having the most appears greedy and having the least seems lame. Crucially, tying for most or fewest is just as undesirable as holding those positions outright.
Condition two is that each person wants to secure as many cookies as possible for themselves. The friends are assumed to be perfectly rational actors, each striving to maximise their outcome based on these rules.
The Step-by-Step Solution
The rational outcome, as determined by logical deduction, is that Andy takes four cookies, Bea takes six, and Celine is left with none.
The workings behind this result are methodical. First, consider Andy's initial move. If he were to take six or more cookies, he would instantly guarantee finishing with the most, violating the paramount first condition. Therefore, he rationally avoids this.
If Andy takes exactly five cookies, he puts Bea in a powerful position. Bea can then take four cookies, securing a middle position for herself (with five left for Celine). This would leave Andy tied with Celine for the most cookies, which fails condition one for him. Thus, taking five is also a losing strategy for Andy.
Andy's Winning Move
This leads Andy to the optimal play: taking four cookies. From this position, Bea analyses her options. If she takes one, two, or three cookies, Celine could simply take four, leaving Bea with the fewest. If Bea takes four or more herself, she would then have the most, or joint most, which is equally unacceptable.
Faced with a scenario where she cannot possibly satisfy the primary condition, Bea's rational fallback is to maximise her haul under condition two. Her best move is therefore to take all six remaining cookies. This leaves Celine with zero, but it fulfils Bea's secondary desire to have as many as possible.
For Andy, taking four is the sweet spot. Taking any fewer would needlessly reduce his total under condition two, while taking four allows him to achieve the middle position he desires. Celine, as the last to act, is left with no viable strategy to avoid having the least, which in this logical framework is an inevitable consequence of the earlier players' optimal moves.
Celebrating Logical Thought
The puzzle was shared as a pre-commemoration of World Logic Day, which falls on January 14. It underscores the fascinating and often unexpected conclusions that emerge from structured logical reasoning. The puzzle creator extended thanks to Deniz Sarikaya of World Logic Day for providing the brain-teaser.
For those who relish such intellectual challenges, harder puzzle sets are available, including dedicated Christmas puzzle competitions. This particular puzzle series has been a regular fortnightly feature for several years, continually seeking out great new logical conundrums for the public to enjoy.
