Sunday Times Teaser 2782 – Spiders

by Graham Smithers

Two spiders at the bottom corner of a rectangular cuboidal barn with sides that are integers in metres want to get to the diagonally opposite corner of the floor without walking across it.

The first takes one of the five shortest paths, two along the floor’s edges, three across the walls and ceiling.

The other climbs vertically to the ceiling and then spins and traverses a straight silk line to the destination.

The total length of its journey is within five centimetres of an integer number of metres.

How high is the barn?