Homework 5 - Hints

3. A number is not greater than itself.

4. Do a proof by contradiction: assume that there is an ordering for the numbers 1 to 36
on the wheel such that every three consecutive integers has a sum of 54 or less. Divide the
wheel into 12 consecutive sections, each containing three (consecutive) integers, and use your
assumption to get an upper bound on the sum of all the numbers on the wheel. You can
actually calculate the sum of the integers from 1 to 36. Recall the formula for the sum of
the integers from 1 to n: n(n + 1)/2. Compare the actual sum to your upper bound.