FourPointsTwoDistances

If you have two coins, flat on a table, you can measure the distance between their centres.

If you have three coins, flat on a table, you can measure the distance between their centres, and because there are three possible pairings (A&B, A&C, B&C) you can get three different answers. Of course, if they're in an equilateral triangle you'll get the same answer for each pair, and if they're in an isosceles triangle then you'll get two different answers, but in general you'll get three different answers.

With four coins there are six possible pairings, so you get up to six different answers. Because the coins are all lying flat on the table you can't get just one answer.

But you can arrange the coins to get just two different answers. Go ahead and try it, pretty much the first thing you'll try will work.

So:

This puzzle was given to me at the MOVES conference in New York in August 2017, where I was lucky enough to spend some time with Peter Winkler, mathematician, puzzle master extraordinaire, and author of "Mathematical Puzzles: A Connoisseur's Collection". One of the thing he said was:

So, there's your challenge.




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