Problems & Puzzles: Puzzles

Puzzle 890. Magic Squares and Pythagorean Triplets On August 8, William Walkington posted the following puzzle in a private mailing list. After his permission I post it here. Find a 3x3 magic square using 3 Pythagorean triplets. His best solution is this one:   3     6    15 12     8      4   9   10      5 "... a semi-magic square, that uses the primitive Pythagorean triple 3-4-5 together with non-primitive Pythagorean triples 6-8-10 and 9-12-15"   Q1. Send your smallest magic solution using only primitive triplets, or demonstrate that these are impossible. Q2. Redo Q1 for a 6x6 magic square and 12 primitive triplets or demonstrate that these are impossible.

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