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Knights and Knaves

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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.
View the archive of all weekly problems grouped by curriculum topic