4. On an island of knights, who always tell the truth, and liars, who always lie, a school was opened. All $2 N$ students of different heights stood in a circle, after which each one said: "I am taller than the student standing opposite me!" How many knights are studying at the school?
Solution. In each pair, one of the two students is indeed taller than their opposite neighbor, so they are telling the truth and are a knight. In total, there are $N$ knights.

Criteria. If the fact that there is definitely one knight in a pair is not justified - 1 point. If a specific example is used as justification - 0 points.