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Power of Multiplication (Posted on 2004-07-16) Difficulty: 2 of 5
A (normal) magic square, containing 9 distinct positive integers, could be made as follows:
2 9 4
7 5 3
6 1 8
Note all rows/columns/diagonals sum to 15.

Can you find the "smallest" multiplication magic square using 9 distinct positive integers where the product of all rows/columns/diagonals are equal?

(One multiplication magic square is smaller than another if its magic product is less than the other's.)

No Solution Yet Submitted by red_sox_fan_032003    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: General solution | Comment 4 of 6 |
(In reply to General solution by Federico Kereki)

Is that a general solution in that there exists an A for any multiplicative magic square?  In particular, the one found so far by Sing4TheDay:

 2  36   3
9 6 4
12 1 18

That is, can we find an A such that each of these numbers is A raised to some integer power? ... or is this a mult magic square that is independent of the proposed general solution?

Certainly we can take the logarithms of these values in any base, and the result will be an additive magic square, but not necessarily in integers.

  Posted by Charlie on 2004-07-16 22:05:41
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