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

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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8 1 6

3 5 7

4 9 2

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

8 9 7

6 3 5

2 4 1

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!

My answer is…

8 9 7

6 3 5

2 4 1

Good job, Mike..

Thanks!!

3 5 7

1 8 9

2 4 6

——————

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

8 9 doesn’t satisfy rule # 5. 8 is not a cubic number. 9 is a cubic number, but the 8 is to the left of it.