## Arithmetic Volume

#### Problem

A sequence is arithmetic if the numbers increases by a fixed amount. For example, 2, 5, 8, are in an arithmetic sequence with a common difference of 3, and if these numbers represented the side lengths of a cuboid, the volume, V = 258 = 80 units^{3}.

How many cuboids exist for which the volume is less than 100 units^{3} and the integer side lengths are in an arithmetic sequence?

Problem ID: 198 (10 Jan 2005) Difficulty: 1 Star