Sunday Times Teaser 3143 – Pipe Fittings
by Peter Good
Published Sunday December 18 2022 (link)
A plumber had three thin metal pipes with square, rectangular and elliptical cross-sections. In order to fit them into his van, he slid the rectangular pipe inside the elliptical pipe and the elliptical pipe inside the square pipe, before placing the pipe assembly in the van. There are four points where the pipes all touch, as shown in the diagram. The maximum and minimum widths of the elliptical and rectangular pipes and the diagonal width of the square pipe were all even numbers of mm less than 1,000, of which one was a perfect square.
What were the five widths (in increasing order)?