# Mathematical Investigation

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Mathematical Investigation

In this report we were asked a number of questions about the solving

of magic squares. The final goal was to fill a magic square in

correctly. The information I was given was about the history of magic

squares and information on how they work. I did not need any extra

information.

Investigation:

What I had to do for this investigation was to fill in a magic square

correctly. I chose to do this by answering the questions given to me

and using my answers to those questions to fill in the magic square. I

did this the way I chose to do it.

Results:

1. The central cell is the only one that touches all the other cells.

Therefore, it is crucial to find the number to place in this cell.

Could you choose any of the numbers to place in this cell? Ask

yourself, could the number 7 be placed in this cell, or the number 1?

You can not put just any number in the central cell of the magic

square because the number has number has to be able to be added to 9

without a repeated number and it has to be added to all other numbers

without crossing the “15” limit. The number 7 could not be placed in

the middle cell because you can only get 3 equations that equal 15

using 7. The problem here is that you need at least 4 solutions: 2

diagonally, 1 horizontally and 1 vertically. The same counts for all

other numbers except for 5. Therefore, the number that should be in

the center cell is 5.

2. There may possibly be restricted on where some of the other umbers

can be placed. The number 9 is the largest to be placed. Could 9 be

placed corner cell? If not, where could it be placed? Think about it