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.

Well, clearly it is infinite.  Among the number of infinite ways are:2011 1's and 2 zeroes2011 1's and 5 zeroes2011 1's and 7 zeroes

Posted by Steve Herman on 2011-04-01 12:27:43