Sunday Times Brain Teaser 777 – Feeler Gauges

by L Poulter

I have half-a-dozen feeler gauges on a ring like keys on a key ring. They are attached in a certain order and by selecting a single gauge or combinations of adjacent gauges it is possible to measure from 1 to 31 thousandths of an inch (thou) inclusive in steps of 1 thou. If I remove two adjacent gauges, replace them with a single gauge and rearrange the five on the ring I can now measure from 1 to 21 thou inclusive in steps of 1 thou with these five gauges by again selecting a single gauge or combinations of adjacent gauges.

What are the thicknesses of the gauges and the order of arrangement on the ring in each case? (start with gauge of unit thickness and then its thinner neighbour for the sets).