Sunday Times Teaser 3076 – Bee Lines
by Nick MacKinnon
Published Sunday September 05 2021 (link)
Three bees are trapped inside three empty cuboidal boxes of different sizes, none of whose faces are squares. The lengths of the edges of each box in centimetres are whole numbers, and the volume of each box is no more than a litre. Starting at a corner, each bee moves only in straight lines, from corner to corner, until it has moved along every edge of its box. The only points a bee visits more than once are corners of its box, and the total distance moved by each bee is a whole number of centimetres. Given the above, the sum of these three distances is as small as it could be.
What is the sum of the distances that the bees moved?