Question 21
We say that a circular arrangement of positive integers is alternating if every number is either smaller, or larger than both of its neighbours. We call a pair of adjacent numbers good if, upon its removal, the remaining numbers form an alternating arrangement.
The numbers $1$ to $300$ are placed on a circle in an alternating arrangement. Determine the least possible number of good pairs of adjacent numbers in such arrangement.
The numbers $1$ to $300$ are placed on a circle in an alternating arrangement. Determine the least possible number of good pairs of adjacent numbers in such arrangement.