Knights and Knaves
Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
Answer: $12$
The first person cannot be telling the truth, since if all the others are knaves, they could not all be lying when they say the person in front of them is a knave.
Therefore the first person is a knave.
The second person says the first is a knave so is telling the truth; he is a knight.
The third says this knight is a knave so he is lying; he is a knave.
Continuing in this way we see that there is an alternating sequence of knave, knight, knave, knight... ending up with $13$ knaves and $12$ knights.