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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 = 2times5times8 = 80 units3.

How many cuboids exist for which the volume is less than 100 units3 and the integer side lengths are in an arithmetic sequence?

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

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