Sunday Times Teaser 2864 – Sequence of Squares
by Victor Bryant
Published August 13 2017 (link)
I started with a rectangle of paper. With one straight cut I divided it into a square and a rectangle. I put the square to one side and started again with the remaining rectangle. With one straight cut I divided it into a square and a rectangle. I put the square (which was smaller than the previous one) to one side and started again with the remaining rectangle. I kept repeating this process (discarding a smaller square each time) until eventually the remaining rectangle was itself a square and it had sides of length one centimetre. So overall I had divided the original piece of paper into squares. The average area of the squares was a two-figure number of square centimetres.
What were the dimensions of the original rectangle?
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