THE DOMINO FRAME PUZZLE.
(
Problems Concerning Games.)
It will be seen in the illustration that the full set of twenty-eight
dominoes is arranged in the form of a square frame, with 6 against 6, 2
against 2, blank against blank, and so on, as in the game. It will be
found that the pips in the top row and left-hand column both add up 44.
The pips in the other two sides sum to 59 and 32 respectively. The
puzzle is to rearrange the dominoes in the same form so that all of the
four sides shall sum to 44. Remember that the dominoes must be correctly
placed one against another as in the game.
Answer:
[Illustration:
+---+-------+-------+-------+-------+-------+-------+-------+
| 2 | 2 | 5 | 5 | 6 | 6 | 6 | 6 | 1 | 1 | | | | | 4 |
| - +-------+-------+-------+-------+-------+-------+---+---+
| 2 | | 4 |
+---+ | - |
| 2 | | 3 |
| - | +---+
| 6 | | 3 |
+---+ T H E | - |
| 6 | | 3 |
| - | +---+
| 3 | | 3 |
+---+ | - |
| 3 | | 1 |
| - | D O M I N O F R A M E +---+
| | | 1 |
+---+ | - |
| | | 1 |
| - | +---+
| 5 | | 1 |
+---+ -S-O-L-U-T-I-O-N- | - |
| 5 | | 4 |
| - | +---+
| 3 | | 4 |
+---+ | - |
| 3 | | 6 |
| - | +---+
| 2 | | 6 |
+---+---+-------+-------+-------+-------+-------+-------+ - |
| 2 | 1 | 1 | 5 | 5 | 5 | 5 | 4 | 4 | 4 | 4 | 2 | 2 | | |
+-------+-------+-------+-------+-------+-------+-------+---+
]
The illustration is a solution. It will be found that all four sides of
the frame add up 44. The sum of the pips on all the dominoes is 168, and
if we wish to make the sides sum to 44, we must take care that the four
corners sum to 8, because these corners are counted twice, and 168 added
to 8 will equal 4 times 44, which is necessary. There are many different
solutions. Even in the example given certain interchanges are possible
to produce different arrangements. For example, on the left-hand side
the string of dominoes from 2--2 down to 3--2 may be reversed, or from
2--6 to 3--2, or from 3--0 to 5--3. Also, on the right-hand side we may
reverse from 4--3 to 1--4. These changes will not affect the correctness
of the solution.
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