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 Counting magic squares (Posted on 2018-06-30)
How many magic squares are there using each the numbers 1 to 9 exactly once?

Show all of them and explain why your set is final.

 Submitted by Ady TZIDON Rating: 2.0000 (1 votes) Solution: (Hide) The numbers sum up to 45, so each row, column and diagonal must add up to 15, forcing number 5 (the average) in the center. 2 7 6 9 5 1 4 3 8 is a possible solution. Call it A. Rotation about the diagonal 258 yields another solution: 2 9 4 7 5 3 6 1 8Call it B. Rotating each of the solutions 90 degrees 3 times , moving number 2 to 3 distinct corners, adds 3 more solutions for A & B each.Rotation about the diagonal 456 creates no new answers. So there are 8 distinct solutions:- 2 & 8 at the ends of one diagonal, 4 & 6 the other, -all even numbers ,

 Subject Author Date Solution Steven Lord 2018-07-12 04:48:37 No Subject Steven Lord 2018-07-12 03:58:54

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