Let's Face It
Problem
Can you place a $4$ by $4$ magic square on each face of a cube so that along each edge of the cube the numbers match?
You can find out more about constructing magic squares and finding different transformations (re-arrangements that preserve the magic properties) in these two articles Magic Squares and Magic Squares II .
Getting Started
How could you change the position of the numbers so that the square is still magic?
Student Solutions
In this problem, you will probably find it helps to do the solution practically. A good way to do this is to draw the net of a cube and to mark a $4$ by $4$ square on each face. Then fill in the numbers for the magic square on one face.
| 1 | 8 | 12 | 13 |
| 15 | 10 | 6 | 3 |
| 14 | 11 | 7 | 2 |
| 4 | 5 | 9 | 16 |
After that you need to work your way over the net, putting a variation of the magic square on each face, and making the numbers coming on the edges of the cube correspond. Then you can make your net into a cube. We'll leave that to you!
This solution to the problem was sent in by Joel of ACS Independent, Singapore.
Here you have the net of a cube with a magic square on each face.
|
13 |
2 |
3 |
16 |
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|
11 |
8 |
5 |
10 |
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|
6 |
9 |
12 |
7 |
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|
4 |
15 |
14 |
1 |
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|
13 |
11 |
6 |
4 |
4 |
15 |
14 |
1 |
1 |
7 |
10 |
16 |
|
8 |
2 |
15 |
9 |
9 |
6 |
7 |
12 |
12 |
14 |
3 |
5 |
|
12 |
14 |
3 |
5 |
5 |
10 |
11 |
8 |
8 |
2 |
15 |
9 |
|
1 |
7 |
10 |
16 |
16 |
3 |
2 |
13 |
13 |
11 |
6 |
4 |
|
16 |
3 |
2 |
13 |
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|
10 |
5 |
8 |
11 |
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|
7 |
12 |
9 |
6 |
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|
1 |
14 |
15 |
4 |
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|
1 |
14 |
15 |
4 |
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|
12 |
7 |
6 |
9 |
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|
8 |
11 |
10 |
5 |
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|
13 |
2 |
3 |
16 |