Suppose that you have a wheel of fortune that has the integers from 1 to 36 painted on it in a random way. Show that regardless of the ordering of the numbers, there are three consecutive (on the wheel) numbers with a sum of 55 or greater. Hint: Think of two different ways to compute the sum of the numbers on the wheel, and then compare the two quantities you get.
I'm pretty much lost on how to do this problem. Some direction would be greatly appreciated.