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.

(In reply to Computer solution by Charlie)

Bravo! And you incidentally also found the one for 945 starting at 10 with length 35 that Tristan and I missed. As you found that there is no number that has exactly 12 nontrivial representations as the sum of consecutive positive numbers, a (very) strict interpretation of the stated question would say that there really is no solution.  However, looser interpreters of language will declare 945 to be the solution even though there are 15 such representations, since it is the smallest number that has at least 12.

Posted by Richard on 2004-06-28 21:52:31