Starting at , and moving anti-clockwise, form consecutive sums consisting of terms:
Then there is at least one of these consecutive sums - call it - that is greater than or equal to the rest. The last term which was reached to form this sum is the required .
The proof depends upon the fact that and that the sum of followed by any number of clockwise terms will be , for one of the other sums, . And since is the greatest sum, will never be negative.