Alex Bellos's biweekly puzzle column delivers a clean set of six questions from Daniel Griller, all built on the same mechanical chassis: people seated in a circle, each making claims about their age relative to their neighbors, and you figuring out how many can possibly be telling the truth. The setup is deceptively simple — three people, one claim each — and then the screws tighten. The first two questions (three people, each claiming to be younger than the person to their left) are warm-ups that force you to notice the cyclical constraint. Around a circle, "younger than the person to my left" can't be true for everyone — the ages have to go somewhere. The minimum and maximum truth-teller counts fall out quickly once you draw the diagram. Questions three and four raise the stakes to seven people making compound claims: younger than the person to my left AND younger than the person two places to my right. Two constraints per person means the seating arrangement has to satisfy a denser web of comparisons. The combinatorial space gets interesting fast. You're no longer just chasing a single ordering — you're juggling overlapping neighborhoods. The final pair — 999 people, each claiming to be younger than the person three places to their left and older than the person three places to their right — is where Griller's design really lands. The "three places" gap creates a modular structure across the circle. Whether you spot the pattern or brute-force small cases first, the puzzle rewards systematic thinking about how local constraints propagate around a cycle. What makes the set work is the escalation. Each pair of questions (max and min truth-tellers) trains a skill that the next pair demands. The jump from 3 to 7 to 999 isn't just showing off big numbers — each size change alters the structural character of the problem. Three is trivial. Seven is tractable by hand. 999 forces you to think in terms of repeating units, not individual seats. Griller's puzzle books — Elastic Numbers and A Ring of Cats and Dogs — trade in exactly this kind of clean combinatorial design: problems that look recreational but require genuine mathematical reasoning. These six questions are a good sample of his style. No trick answers, no lateral-thinking gimmicks, just careful logic applied to a well-defined structure. The column's no-spoilers policy is doing real work here. If you want the solutions, Bellos posts them the same day at 5pm UK time. In the meantime, the puzzles are worth working through with pen and paper. The round table is doing more than you think.
