One of the oldest puzzles appears to be the construction of the Lo Shu, a magic square of order 3 devised in China well before the Common Era—more than four thousand years ago, according to legend.
In this square, the numbers 1 to 9 are arranged so that the three numbers in any row, column or diagonal always add up to the same total: 15. Although the sheer beauty of this mathematical object—the only one of order 3, up to rotations and reflections—probably gave its creator aesthetic pleasure, it was later appropriated by magicians and occultists of every stripe, hence the name "magic" (see our features "The arithmetic of magic squares", Tangente 161, 2014, and "Magic squares", Tangente 196, 2020).
In China, Greece, India…
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Neither the age nor the simplicity of this arrangement prevents present-day enthusiasts from discovering new relationships within it. The following identities were published by R. Holmes in the Mathematical Gazette in 1970:
