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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.
Knights and Knaves
Age 11 to 14
ShortChallenge Level 
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.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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