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. What’s the absolute right answer? I need to know!!!!!!!

  2. Hi how would I arrange the digits from 10 to 18 in a 3×3 table so that every row, column and diagonal totals the same amount? With explanation please!

  3. My answer is…

    8 9 7
    6 3 5
    2 4 1

    Good job, Mike..

  4. 3 5 7
    1 8 9
    2 4 6

  5. Mike Sprayberry

    ——————
    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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