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I'm trying to help my daughter with her homework. I'm not looking for an answer, but the process.

She has been asked to solve this:

[ [   ?,  36,   ? ]
  [   9,   6,   4 ]
  [ -12,   ?,   ? ] ]

My approach was to substitute letters for the missing values:

[ [   A,  36,   B ]
  [   9,   6,   4 ]
  [ -12,   C,   D ] ]

Then I could solve for the unknowns:

  9 +  6 + 4 = 19
  A + 36 + B = 19
-12 +  C + D = 19
...

Solving the equations resulted in most of the rows, columns and diagonals adding up to 19 - however, not all did. I ended up with:

A = -42
B = 25
C = -24
D = 55

I'm not clear where I'm going wrong.


My Math knowledge is very poor, simple clear answers will be preferred over complex answers.

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  • $\begingroup$ Did the problem state it was a magic square? $\endgroup$ – Bram28 Oct 7 '17 at 15:12
  • $\begingroup$ Yes - source: corbettmaths.files.wordpress.com/2013/02/… $\endgroup$ – Chris Snow Oct 7 '17 at 15:13
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    $\begingroup$ Note that the referenced file says that the product, not the sum, should be constant. $\endgroup$ – rogerl Oct 7 '17 at 15:14
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    $\begingroup$ Ah! So you need to make sure that the product is the same in each row, column, and diagonal, rather than the sum! I;m sure your daughter can do this. :) $\endgroup$ – Bram28 Oct 7 '17 at 15:15
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    $\begingroup$ It takes two days before I can accept my own answer. Happy to accept someone else's answer. $\endgroup$ – Chris Snow Oct 7 '17 at 15:27
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As per the comments, the products, not the sums, of the rows and columns should be the same.

Apart from that, I think it's a bit cumbersome to introduce so many variables and equations. Just solve the values one at a time. For example, the second row has product $4\cdot6\cdot9$, so the missing entry in the second column must be $1$, etc.

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