As the calendar flips to January, a unique celebration awaits those who prize clear thinking. January 14 marks World Logic Day, a Unesco-endorsed event dedicated to promoting the study and practice of deductive reasoning. To mark the occasion, a fiendish new puzzle challenges you to apply pure logic to a simple-sounding scenario involving cookies and cunning friends.
The Premise of the Puzzle
Three friends—Andy, Bea, and Celine—find themselves with a jar containing ten cookies. They agree to a game. They will take turns, starting with Andy, then Bea, then Celine, reaching into the jar to take cookies for themselves. On each turn, a player may take as many cookies as they wish. However, they are bound by two critical conditions that govern their rational choices.
Firstly, no one wants to finish with the most, or the fewest, cookies. Ending up with a joint most or joint least is considered just as undesirable as having an outright majority or minority. Secondly, each friend naturally wants to secure as many cookies for themselves as possible. Crucially, the first condition takes strict priority over the second. The friends cannot communicate or form alliances, and they are all assumed to be perfectly rational actors seeking their best outcome.
Applying Rational Strategy
The puzzle, provided by Deniz Sarikaya for World Logic Day, requires solvers to step into the minds of the three players. One must consider the implications of each possible move from the first turn, working backwards from the end of the game. With ten cookies in play and the strict social aversion to being the 'greedy' or 'lame' outlier, the solution is not immediately obvious.
The challenge lies in balancing the conflicting desires: the paramount need to avoid an extreme position, and the secondary drive to maximise personal gain. It is a classic exercise in game theory and strategic foresight, where anticipating the reactions of others is key. The friends do not have to take all the cookies, and one or more could theoretically take none, adding another layer of complexity to their calculations.
Celebrating the Power of Reason
World Logic Day serves as an annual reminder of the importance of logical thinking in academia and everyday life. A host of events are organised globally to celebrate the field. For those who find this cookie conundrum too light a warm-up, the Royal Statistical Society's Christmas Puzzle competition offers a more formidable test of mental mettle.
This puzzle continues a long-running series set by Alex Bellos, who has been presenting alternate Monday brainteasers since 2015. The solution to the cookie jar dilemma will be revealed later today. In the meantime, the puzzle stands as a fitting tribute to the clear, structured thought that World Logic Day aims to promote.
