Question 19
The natural numbers from $1$ to $300$ inclusive are placed around a circle. We say that such an arrangement is *alternating* if each number is smaller than both of its neighbours or larger than both of its neighbours. We call a pair of neighbouring numbers a *good pair* if, after removing that pair from the circle, the remaining numbers form an alternating arrangement.
Determine the smallest possible number of good pairs in an alternating arrangement of the numbers from $1$ to $300$ inclusive.
Determine the smallest possible number of good pairs in an alternating arrangement of the numbers from $1$ to $300$ inclusive.