Sunday Times Teaser 2654 – Square Cut

by Andrew Skidmore

I started with a rectangular piece of paper one metre long and more than half a metre wide and used a single straight cut to divide it into a square and a remainder.

I took the remainder and cut it in the same way to produce another square and a remainder.  I did this repeatedly until the remainder was itself a square.

As a result the original rectangle had been divided into six squares whose sides were all whole numbers of centimetres.

What was the width of the original piece of paper?