Arrange the numbers 1-9 in a 3×3 square using each only once

Brain Teaser for Engineers

Arrange the numbers 1-9 in a 3×3 square using each once only, according to the following rules:

  • exactly one prime number is directly above a prime number that’s two numbers less;
  • each pair of opposite corners sums to the same square total and exactly two columns share another square total;
  • exactly one prime number is directly to the left of a non-prime number that’s two numbers greater;
  • directly above exactly one square number is a number that’s four numbers greater; and
  • directly to the right of exactly one cubic number is a number that’s one number greater.

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    10 Comments

    1. ——————
      8 9 7

      6 3 5

      2 4 1
      ——————

      Proof follows:

      7
      5 satisfies rule #1

      8 _ 7
      _ _ _
      2 _ 1 satisfies Rule #2a (3 squared)

      8 9
      6 3
      2 4 satisfies Rule #2b (4 squared)

      2 4 satisfies Rule #3

      5
      1 satisfies Rule #4

      8 9 satisfies Rule #5

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