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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?

2 Comments Leave one →
  1. brian gladman permalink

  2. ahmet cetinbudaklar permalink

    Drawing squares of axa , axa , axa , (3a)x(3a) , (3a)x(3a) and (7a)x(7a) we get:

    (7a)x100=49x(a^2)+9x(a^2)+9x(a^2)+a^2+a^2+a^2=70x(a^2) giving us the value of a hence the answer as 7a

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