**From New Scientist #1185, 13th December 1979** [link]

Scalenia is a country bounded by three straight frontiers – called *A, B* and *C,* of course – each of a different length but each an exact number of kilometres long. The curious thing is that the length of *A+B+C,* and the lengths of *A+B−C, A+C−B* and *B+C−A* are all precisely square numbers of kilometres.

If Scalenia has the smallest perimeter consistent with this curious fact, what is the length of each of its frontiers?

[enigma43]

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Solution:The frontiers are 26km, 80km and 90km in length.