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A puzzle by George Glaeser: fit the following 28 dominos:
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on the (7 x 8) matrix
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| 3 | 6 | 2 | 0 | 0 | 4 | 4 |
| 6 | 5 | 5 | 1 | 5 | 2 | 3 |
| 6 | 1 | 1 | 5 | 0 | 6 | 3 |
| 2 | 2 | 2 | 0 | 0 | 1 | 0 |
| 2 | 1 | 1 | 4 | 3 | 5 | 5 |
| 4 | 3 | 6 | 4 | 4 | 2 | 2 |
| 4 | 5 | 0 | 5 | 3 | 3 | 4 |
| 1 | 6 | 3 | 0 | 1 | 6 | 6 |
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Solution:
Below is the solution. An exhaustive search shows that
the matrix A can be covered in exactly one way by the
28 dominos (i,j), 0 < i <= j < 7.
We call the 7x8 matrix a Glaeser matrix.
You can run the Mathematica Source yourself.
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The Glaeser Puzzle shows that for n=7, there is a Glaeser Matrix.
For n=2, there is no Glaeser Matrix: the
3 Glaeser dominos (0,0),(1,1),(0,1) can not be arranged uniquely on
a 2 x 3 board. For n=3, there is a Glaeser matrix:
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