Integers equal to each other or differing by 1 will be called "almost equal " within the contents of this problem.

In how many ways can 2011 be expressed as a sum of almost equal addends?
The order of the addends in the expression is immaterial.

(In reply to April Fool's answer by Steve Herman)

Your answer fits the date PERFECTLY.

On a more POSITIVE note, allow me to rephrase the question:

In how many ways can 2011 be expressed as a sum of almost equal  POSITIVE addends?

New answer  is welcome!

Posted by Ady TZIDON on 2011-04-01 13:39:56