## The hardest logic puzzle ever

As promised yesterday… Raymond Smullyan has created ever-more-baroque variants of the following problem:

Two guardians watch over a fork in the road. One path leads to safety, the other to a grisly death. One of the guardian is a knight, meaning that he always tells the truth. The other is a knave, meaning that he always lies, answering “yes” to questions whose correct answer is “no”, and vice versa. You do not know which guardian is a knight and which is a knave. With a single question, how will you find the safe path?

If you don’t know the answer, turn away now, because it’s going to get a lot stickier from here. If you do know the answer, then try this, sometimes called the hardest logic puzzle ever posed…

There are three guardians, A, B and C. Their names are Knight, Knave and Chaos. Knight always speaks truly, Knave always lies. Chaos tossed a coin this morning to decide whether today he would behave like Knight or like Knave.
Your task is simple: ask three yes-no questions, each of a single guardian, and determine which is Knight, which is Knave, and which is Chaos. There is, alas, a complication: the guardians understand English but will answer in the local language, in which “Da” means yes and “Ja” means no. Or possibly “Ja” means yes and “Da” means no – you cannot remember.

I’ll be back tomorrow with a hint. Have fun. One more thing: I enjoy Richard Wiseman’s regular puzzles and I’ll follow his rule: don’t reveal the solution in the comments. If you’ve solved it – without resort to Google – then by all means tell us that you’ve done so – but please don’t spoil the fun by revealing the solution.

EDIT: A clarification – the three guardians do know each others’ identities, but not necessarily the result of Chaos’s coin flip. And someone has written to say there’s a wikipedia page on this problem. Of course there is: it’s the hardest logic puzzle ever. But looking at the wikipedia page does not actually count as solving it…

EDIT 2: As mentioned yesterday, that Smullyan book again: http://www.amazon.co.uk/What-Name-This-Book-Dracula/dp/0140135111

EDIT 3: (Wow – these puzzles are hard to state accurately in plain English!) To clarify, if Chaos has decided to behave like Knight, that means he answers yes-no questions truthfully, not that he will claim to be Knight, etc.

Share

### Tim Harford’s blog

This blog is no longer updated but it remains open as an archive.

Tim, also known as the Undercover Economist, writes about the economics of everyday life.

### The Undercover Economist: a guide

Publishing schedule: Excerpts from "The Undercover Economist" and "Dear Economist", Tim's weekly columns for the FT Magazine, are published on this blog on Saturday mornings.
More about Tim: Tim also writes editorials for the FT, presents Radio 4's More or Less and is the author of "The Undercover Economist" and "The Logic of Life".