Math Is Fun Forum

mathsabc123

Guest

magic squares?

i need help for 'magic squares' puzzles. basically, each of the numbers in each row, column and diagonal line must add up to a certain number. i have no idea how to solve this, i have tried many different options.

1)

? ? -17 -7
? -9  ? -12
-11 -13 ? ?
-16 ? -5 ?

2)

? ? -15 -5
-13 ? ? -10
? -11 -12 ?
-14 -4 ? ?

3)

? ? -9 1
? -1 ? -4
-3 -5 ? ?
-8 ? 3 ?

sorry for the bad layout. i'm not good at trial and error..

mathsabc123

Guest

Re: magic squares?

solved number '3'.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: magic squares?

I LaTeXified all of those squares to make them easier to read.

1.

2.

3.

As for actually solving them, you'd first want to find out what all the rows and columns total. Then you'd be able to fill in any row, column or diagonal that already had 3 numbers, and it would be much easier to compare other rows. I'll try to do them later, if they haven't already been done.

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Why did the vector cross the road?
It wanted to be normal.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: magic squares?

OK, forget what I said earlier about finding out what all the rows, columns, etc. need to add up to. The diagrams below show 4 specific squares in each puzzle. Each of those squares is not already filled in, and in each case, they occupy exactly one of each row, column and diagonal. So by adding 1 to each of those squares, you can change the whole puzzle value.

So now the strategy is to just pick a value that you want everything to add to, and then fill it in to make it work.

    1.           2.            3.
    x000       0x00       x000
    00x0       00x0       00x0
    000x       x000       000x
    0x00       000x       0x00

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Why did the vector cross the road?
It wanted to be normal.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: magic squares?

When I've seen magic squares, they usually tell you the "magic number" and you have to make each row/column/diagonal add up to that number.  It looks like in this case, you can make the magic number whatever you want.   Let's pick -36 for the first one.   Now that we have the magic number, we can figure out A in the diagram below: -16 + -13 + A + -7 = -36;  So A is 0.   Now that you filled in A, you have enough information to figure out B, then C, etc.

Here it is solved for magic number of -36

You can use the same procedure to solve the other two puzzles.   In each case, you only have one missing number in the diagonal going from top-right to bottom left.   Replace the ? in that diagonal (2nd row, 3rd column) with whatever number you want (I picked 0 just to make it easy), find out the sum of the diagonal, and then continue on filling in the remaining spaces.