[A lion and its tamer]

If I remember well, if the tamer runs on the perimeter, the lion catches the tamer.

If the lion follows the radius of the tamer, his trajectory is a 1/2 circle and not a spiral. He catches the tamer in a finite time.

Then, he has an escape strategy that works for an infinite time.

[perfect powers]

The answer depends whether you accept 0 as a square and whether you accept the same number twice.

[perfect powers]

A bit cheating, but one candidate would be 125= 0² + 5² + 10² = 3² + 4² + 10² = 5² + 6² + 8²

[Having sisters]

According to chinese rules that held for a long time, you can have only one child. But if it is a girl, you can have a second one.

If the rules are respected, out of 4 families, 2 have one boy only, 1 has one boy and one girl, 1 has two girls.

The 3 boys have 1/3 sister on average, the 3 girls have 2/3 sisters on average.

Since China represents a non-negligible proportion of the world population, it would seem girls have more sisters on average.