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| Math Central | Quandaries & Queries |
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Question from Mika, a student: 7th grader wanting to find solution to magic square: place the integers from -5 to +10 in the magic square so that the |
Hello Mika,
There is a nice procedure for constructing such magic squares:
Fill the table, from left to right and top to bottom, starting with the lowest number.
-5 |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Now erase every number not in a diagonal.
-5 |
|
|
-2 |
|
0 |
1 |
|
|
4 |
5 |
|
7 |
|
|
10 |
Note that the two diagonals add up to our magic number, 10.
Now, similar to before, we fill in the rest of the table, from left to right and top to bottom, with the numbers we have not used, except now starting from the greatest.
The first couple lines fill in as follows,
-5 |
9 |
8 |
-2 |
6 |
0 |
1 |
3 |
|
4 |
5 |
|
7 |
|
|
10 |
Filling in the rest leaves you with a magic square, TA DA!! Can you see how this magic trick is done?
Tyler
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