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Knights and Knaves

Age 11 to 14 Short Challenge Level:

A magical island is inhabited entirely by knights (who always tell the truth) and knaves (who always tell lies).

One day 25 of the islanders were standing in a queue.

The first person in the queue said that everybody behind was a knave.

Each of the others in the queue said that the person immediately in front of them in the queue was a knave.

How many knights were there in the queue?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.