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.


Records   |  Conjectures  |  Problems  |  Puzzles