Enigma 278: Uncle Pinkle’s new system
From New Scientist #1425, 11th October 1984 [link]
Uncle Pinkle has moved house, and he is installing a new triphonic audio-system on his garden lawn. This system consists simply of three transmitters A, B and C, each of which is to be exactly M yards from the others.
Uncle Pinkle will sit at a point X, carefully chosen so that the distances XA, XB and XC are exact whole numbers of yards.
X must not be in a direct line with any pair of transmitters. [*]
The total XA + XB + XC is to be as small as possible.
Uncle Pinkle asks me to specify M, and the distances XA, XB and XC, to meet his requirements.
Can you help please?
(If you find yourself using a calculator, let alone a computer, you are getting much too big. The rule in italics [*] is not as big a handicap as you may be thinking).