Question 27
$N$ boys ($N \ge 3$), no two of them having the same height, are arranged along a circle. A boy in the given arrangement is said to be *middle* if he is taller than one of his neighbors and shorter than the other one.
Prove that if $N$ is odd number then there exists at least one middle boy in any arrangement of the boys along the circle.
Prove that if $N$ is odd number then there exists at least one middle boy in any arrangement of the boys along the circle.