I‘m not entirely sure, how to show the following statement:
An arc B with a circumference of $24$ is drawn between K1 and K2 on a circle in the plane with a circumference of $42. 21$ people mark circular arcs of length $4$ on B clockwise. Prove that there must at least be one point on B that belongs at least $5$ different arcs of length $4$ marked by the people.
Now, according to my understanding the statement I’m supposed to show, is wrong.
$\frac{24}{4} = 6, 3 \lt \frac{21}{6} \lt 4$
Therefore, it should be possible for the $21$ persons to mark their arcs in such a way, that every point on the arc is marked by at most $4$ people. But then the statement I’m supposed to prove would be false. Maybe the situation would be different, if no two arcs marked by the people could be completely identical, but I don’t think that it says so anywhere in the problem. We are supposed to prove this using the pigeonhole-principle.
I hope someone can help me.