# Solving magic square results in incorrect answer

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.

• Did the problem state it was a magic square? – Bram28 Oct 7 '17 at 15:12
• Yes - source: corbettmaths.files.wordpress.com/2013/02/… – Chris Snow Oct 7 '17 at 15:13
• Note that the referenced file says that the product, not the sum, should be constant. – rogerl Oct 7 '17 at 15:14
• 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. :) – Bram28 Oct 7 '17 at 15:15
• It takes two days before I can accept my own answer. Happy to accept someone else's answer. – Chris Snow Oct 7 '17 at 15:27

## 1 Answer

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.