The Queen of Hearts has lost her tarts! She is sure that those knaves who have not eaten the tarts will tell her the truth and the guilty knave will tell lies. When questioned the five knaves declare:

Knave 1
One of us ate them

Knave 2
Two of us ate them

Knave 3
Three of us ate them

Knave 4
Four of us ate them

Knave 5
Five of us ate them

How many of the knaves were honest?

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