This coming week marks an annual celebration dedicated to the art of clear thinking. World Logic Day, a UNESCO-approved event on January 14, promotes the vital study of deductive reasoning. To mark the occasion, we present a deliciously tricky puzzle to sharpen your mind.
The Cookie Conundrum: A Test of Rationality
Three friends—Andy, Bea, and Celine—face a classic strategic dilemma. They have a jar containing ten cookies and will take turns helping themselves. The order is fixed: Andy goes first, then Bea, then Celine. On each turn, they may take as many cookies as they wish from the jar.
The friends are bound by two clear, yet potentially conflicting, desires. Their primary goal (Condition 1) is to avoid finishing with either the most or the fewest cookies. Sharing the top or bottom spot is just as undesirable as holding it outright. Their secondary goal (Condition 2) is simple: to get as many cookies for themselves as possible.
Crucially, Condition 1 overrides Condition 2, though both are desirable. The friends cannot communicate or form alliances. They are perfectly rational actors, and the jar does not need to be emptied.
Deduction in Action
This puzzle, courtesy of Deniz Sarikaya of World Logic Day, challenges you to think several steps ahead. It requires the same cool, logical reasoning famously employed by Star Trek's Mr. Spock. The solution relies on backward induction—working out what a rational player would do on the final move, and then reasoning backwards to the first.
While we await the official solution, it's a perfect time to reflect on the illogical arguments we encounter daily. From political spin to flawed advertising claims, the world is full of examples where emotion trumps reason. World Logic Day serves as a timely reminder of the power and elegance of sound deduction.
For those seeking more mental gymnastics, the Royal Statistical Society’s Christmas Puzzle competition offers a formidable challenge. Meanwhile, puzzle aficionado Alex Bellos continues his long-running series of fortnightly brainteasers, always on the hunt for great new puzzles.
