The Round-Table Truth-Teller Puzzles: Solutions and Reasoning

A weekly puzzle column presents three age-based logic problems involving people seated around circular tables. Each participant claims, “I am younger than the person to my left,” or, for the seven-person version, adds The challenge is to determine the maximum and minimum possible numbers of truth-tellers for each table size.

The Guardian

• Three-person table – Because the oldest individual must lie, at most two participants can be truthful. An arrangement such as ages 30 – 40 – 20 (clockwise) yields two truth-tellers. Conversely, the youngest must tell the truth, so the minimum is one truth-teller; ages 40 – 30 – 20 achieve this.

The GuardianThe Guardian

• Seven-person table – Logical analysis shows the two oldest must lie, eliminating the possibility of six or seven truth-tellers. A configuration with ages 10 – 20 – 40 – 70 – 30 – 50 – 60 produces four truth-tellers, which is the greatest attainable number. The youngest must be truthful, so the smallest possible count is one; arranging ages in strict descending order (70 – 60 – 50 – 40 – 30 – 20 – 10) leaves only the youngest honest.

The Guardian

• 999-person table – By partitioning seats into three repeating colour groups (gold, silver, bronze) and applying the same reasoning to each, all but six participants can be truthful. An age-increasing sequence around each colour yields 993 truth-tellers as the maximum. If ages decrease clockwise, every statement is false, giving a minimum of zero truth-tellers.

The Guardian

The puzzles are featured in a long-running science-culture column that has appeared on alternate Mondays since 2015. The author of the day’s puzzles, Daniel Griller, is also known for the puzzle books *Elastic Numbers* and *A Ring of Cats and Dogs and Other Curious Puzzles*. The column invites readers to discuss the problems while withholding solutions until later in the day.

The Guardian

• “I am younger than the person to my left.” — Each

The Guardian

• “I am younger than the person to my left, and I am younger than the person two places to my right” — Each

The Guardian