"it was proved later by the best minds of the Department that there do not exist sets of numbers with the required properties"

Is it becasue that when k=25,the minimal set of numbers is {2,4,6,8,...50}???So we can't find a solution with every number within 49?

If I'm right,why does the problem says "it was proved by the best minds of the Department "?It's so obvious...

It's a joke, you know ;)