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Counting magic squares (Posted on 2018-06-30) Difficulty: 2 of 5
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 8
Call 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 ,

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSteven Lord2018-07-12 04:48:37
No SubjectSteven Lord2018-07-12 03:58:54
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