The integer 30 can be written as a sum of consecutive positive integers in three ways:
30 = 9+10+11 = 6+7+8+9 = 4+5+6+7+8.

Find the smallest positive integer which can be written as a sum of consecutive positive integers in 12 ways.

I have a theory, and no time to prove it now, that the answer is far smaller than 1890.  I think the answer is 105.  I will verify and, if it holds up, explain later...

Posted by Bryan on 2004-06-28 17:51:37