by Andrew Skidmore

Published Sunday April 26 2026 (link)

Liam is designing a logo as part of a school project. He has drawn a circle that touches all the sides of an octagon. The side lengths of the octagon are all different two-figure numbers of mm; in fact, they are all triangular numbers (ie, numbers of the type 1+2+3+4+…). Taken together these numbers use all the digits 0 to 9 (at least once each). If I told you the value of one of the lengths that is an odd number, then you would be able to answer the question below.

What (in mm) is the perimeter of the octagon?