Solution to Problem 270

Correct solutions came from John Snyder, USA; Farid Lian, Colombia; Brian Bradie, USA; Ahron Teitelman, Israel; Aaron Lo Cascio, USA; Alejandro Vellano, Argentina; Dan Dima, Romania; Eric Pittelkau, USA; Bill Webb, USA; Jean Moreau de Saint-Martin, France; Ahmed AboAdham; Ron Welch, USA; Claudio Baiocchi, Italy; Lou Cairoli, USA; Kai Grinde Myrann, Norway; Gary Smith, USA; Micah Thurn, Bradley University; Matt Meyer, Bradley University; Philippe Fondanaiche, France; Steven Young, USA; Francesc Suņol, Spain; Agustin Arrieta, Spain.

There are five ways to write 2007 as the sum of consecutive positive integers (six if you count the trivial one-term sum).

Adding the k integers starting with s yields k(2s+k-1)/2. For this to equal 2007, k must be a divisor of 4014. For six of the possible values of k (including 1), the corresponding value of s is positive.

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ã2007 Alberto L. Delgado