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Allan Adler's

Multiplying Magic Squares - page 2



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Suzanne's Magic Squares || Multiplying Magic Squares: Contents || Exploring the Math
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The Plan

It is easier to visualize the product of the two magic squares if guidelines are added to break the 12x12 square up into 3x3 blocks.



As you can see, we have a 4x4 (i.e. the size of B) array of 3x3 (i.e. the size of A) squares.

The basic plan is to make a big empty 4x4 grid and fill each of its empty cells with a 3x3 magic square.

    Check for Understanding:

    1. How many squares are in each row?
    2. How many squares are in each column?
    3. How many numbers are in each row of one of the squares?
    4. How many numbers are in each column of one of the squares?

The Grid

Start with a big empty 4x4 grid:



Now recall magic square B:



Question: Where is the number 1?

Answer: In the upper left cell.

    Check for Understanding:

    1. How many cells are there in the original 4x4 magic square (square B)?
    2. How many cells are there in the big empty 4x4 grid?

Step One

Find the corresponding (upper left) cell in the big empty 4x4 grid and put a copy of square A there.



Continued next page.



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