Solving magic square results in incorrect answer

Question

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.

Yes - source: https://corbettmaths.files.wordpress.com/2013/02/negatives-multiplication-and-division.pdf — Chris Snow, Oct 07 '17 at 15:13
Note that the referenced file says that the product, not the sum, should be constant. — rogerl, Oct 07 '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 07 '17 at 15:15
Is there a way to mark a question as answered when the answer is only from comments? — Zubin Mukerjee, Oct 07 '17 at 15:18
@ZubinMukerjee I don't know ... I've had the same thought many times myself; it would be nice to be able to get questions out of the 'Unanswered' queue! — Bram28, Oct 07 '17 at 15:22
just post your point in the answers box and have the asker accept it. — , Oct 07 '17 at 15:25
It takes two days before I can accept my own answer. Happy to accept someone else's answer. — Chris Snow, Oct 07 '17 at 15:27
I think it's possible to mark the answer as a "community answer" but I'm not sure what the etiquette is on that ... I guess it doesn't really matter — Zubin Mukerjee, Oct 07 '17 at 15:27

score 4 · Accepted Answer · answered Oct 07 '17 at 15:28

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.

Solving magic square results in incorrect answer

1 Answers1