Sharpen your mind and raise an eyebrow in honour of World Logic Day, the UNESCO-approved annual celebration of deductive reasoning that falls on January 14. To mark the occasion, we present a deliciously tricky brainteaser designed to test your strategic thinking against the cold, hard rules of logic.
The Cookie Conundrum: A Test of Rational Self-Interest
Three friends—Andy, Bea, and Celine—face a classic game theory dilemma. They have a jar containing ten cookies and will take turns, in that order, to help themselves. On each turn, a person may take as many cookies as they wish, from none to all that remain. However, they are bound by two clear, hierarchical conditions that govern their rational choices.
Firstly, and with top priority, no one wants to finish with the most or the fewest cookies. Crucially, tying for the most or the least is considered just as undesirable as holding those positions outright. Secondly, and only after the first condition is satisfied, each person wants to secure as many cookies for themselves as possible.
The Rules of the Game
The scenario presents a pure test of backward induction and rational choice. The friends cannot communicate or form alliances. They do not have to take all the cookies, and one or more could theoretically take none. The puzzle, set by Deniz Sarikaya for World Logic Day, asks a simple question: given that all three act perfectly rationally and in their own best interest, how many cookies does each person end up with?
The solution hinges on the absolute priority of Condition 1 over Condition 2. Avoiding the social stigma of being the greediest or the lamest is paramount; maximising cookie intake is a secondary concern. This creates a fascinating chain of reasoning that each player must work through from the final move backwards.
For those seeking an even greater challenge, the article points towards the Royal Statistical Society’s Christmas Puzzle competition. Meanwhile, the solution to this cookie-sharing puzzle will be revealed later today.
So, before the answer is published, why not wrestle with the logic yourself? It’s the perfect way to celebrate the intellectual rigour that World Logic Day promotes. And while you ponder, perhaps reflect on your favourite illogical arguments—the amusing leaps of faith and flawed syllogisms we encounter in everyday life that make the clarity of good logic so valuable.
