MATH CHALLENGE

At some arm wrestling championship, the champion had to face at least one opponent per hour, but had no more than 125 meetings over a period of 75 hours. (Here one hours means a period starting at an exact time and going to the next hour.) Knowing this, show that there is a period of consecutive hours during which the champion had exactly 24 matches.

I've reduced the problem to
Given
x1+x2+...+x75 <= 125
x1,x2,...,x75 >= 1
Prove that
Exists a subset B of {x1,...,x75} such that sum(B)=24