Question 20
Arrange the numbers $1, 2, \ldots, 32$ in a sequence such that the arithmetic mean of two numbers does not lie between them. (For example, $\ldots, 3, 4, 5, 2, 1, \ldots$ is invalid, because $2$ lies between $1$ and $3$.) Can you arrange the numbers $1, 2, \ldots, 100$ in the same way?