Enigma 1686: Squaring the circle
22 February 2012
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From New Scientist #2853, 25th February 2012 [link]
A builder was contracted to pave a circular courtyard with square paving slabs having sides of length 1 metre. The radius of the courtyard was an exact number of metres. The slabs had to be laid in a rectangular grid with no gaps, and with four slabs meeting at the centre of the circle. The slabs at the edge obviously had to be cut, but the builder had to cut as few slabs as possible.
When he was finished, the builder found he had cut exactly a third of the slabs (he didn’t re-use any of the discarded pieces).
How many slabs were used, and what was the radius of the courtyard?