Midway though the new Sally Rooney novel, Intermezzo, two of the characters discuss a puzzle about hats. I thought it would make a perfect puzzle for this column, so here it is.
A liar who always lies says “All my hats are green.”
Can we conclude that he has some hats?
In fact, I would like to extend the puzzle by making it multiple choice. Which, if any, of the following statements can we conclude from what the liar has said?
A) The liar has at least one hat.
B) The liar has only one green hat.
C) The liar has no hats.
D) The liar has at least one green hat.
E) The liar has no green hats.
Note: this question was originally set in a maths exam, so the answer assumes some basic assumptions about formal logic. A liar is someone who only says false statements.
I’ll be back at 5pm UK with the solution. PLEASE NO SPOILERS. Instead please discuss other logic puzzles that have appeared in literary works.
UPDATE: Read the solution here.
Looking for a Christmas gift for the puzzle lover in your life? My latest book is Think Twice: Solve the Puzzles That (Almost) Everyone Gets Wrong, a collection of counter-intuitive conundrums that make you think about thinking – while enjoying the pleasure of being misled.
Think Twice: Solve the Simple Puzzles (Almost) Everyone Gets Wrong. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply. (In the US, the book is called Puzzle Me Twice.)
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
