Professor Stewart's Hoard of Mathematical Treasures
“If only to check they still had them.
He held up four coins, identical gold pieces-of-eight.
‘Now, me lads - what I wants ye to do is to place these four gold coins so that they be equidistant.’ Seeing the baffled looks on their faces, he explained. ‘What I means, lads, is that the shortest distance between any two coins’as to be the same as that between any other two coins.’ To his considerable surprise, the bosun immediately realised that it was no good ‘working in the plane’, and the solution required three dimensions of space. He quickly found an answer: place three of the coins touching each other in a triangle, and sit the fourth on top. All coins are touching, so all distances between them are zero, hence equal.
How to do it with four coins.
Redbeard, dismayed, thought for a moment. ‘So, ye think ye be smart? Try doin’ it with five coins, then. Make them all equidistant from each other!’ Eventually the bosun found an answer, but it wasn’t easy. What was it?
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