Prime Magic - Futility Closet

Prime Magic

berloquin prime puzzle

In his 1976 book 100 Numerical Games, French puzzle maven Pierre Berloquin asks whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):

1 2 3 5 7 11 13 17 19

Is it?

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No. The numbers total 78, so in a successful magic square each row and column would total a third of that, or 26. But only one of the primes is even, which means that in two rows and two columns we’d have to produce an even number by adding three odd numbers, which is impossible.

June 14, 2017June 18, 2017 | Puzzles