You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page...

problem icon

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Knights and Knaves

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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.

Theerfore 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.

This problem is taken from the UKMT Mathematical Challenges.