Nick writes the numbers \(1,2,\dots,33\), each exactly once, at the vertices of a polygon with \(33\) sides, in some order.
For each side of the polygon, his little sister Hannah writes down the sum of the two numbers at its ends. In total she writes down \(33\) numbers, one for each side.
It turns out that when read in order around the polygon, these \(33\) sums are \(33\) consecutive whole numbers.
Can you find an arrangement of the numbers written by Nick that makes this happen?