Let's Face It
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 .
How could you change the position of the numbers so that the square is still magic?
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 |