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The Central Cell (Posted on 2004-04-16) Difficulty: 2 of 5
Prove that the central cell (the number in the middle cell) of any 3x3 magic square is always one-third the magic constant (the sum of any side, either 2 major diagonals, or either center row in the magic square).
Show that in any larger square (n x n), the central cell does not need to be 1/n the magic constant.

See The Solution Submitted by Victor Zapana    
Rating: 4.5000 (4 votes)

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re(2): Solution to part 1 | Comment 7 of 11 |
(In reply to re: Solution to part 1 by e.g.)

e.g.,

It most certainly does not suffice.

If the problem said "Show that in ALL larger sqaures (nxn), the central cell does not need to be 1/n, the magic constant", then it would suffice.  But the problem doesn't say that.

To address this issue, one must either:

  • show that for ALL cases of (nxn) where n is odd and larger than 3, then the center square need not be 1/n x the magic constant, or
  • refute part 2 by showing that there is a larger square where n is odd and that the center actually MUST be 1/n x the magic constant

  Posted by SilverKnight on 2004-04-16 18:16:33
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