198 Domino Puzzles
the twenty-eight dominoes exactly as shown in the illustration, where the pips
are omitted, so that the pips in everyone of the seven columns shall sum to
24, and the pips in everyone of the eight rows to 21. The dominoes need not
be 6 against 6, 4 against 4, and so on.
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- • • • 492. THE DOMINO COLUMN
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Arrange the twenty-eight dominoes
in a column so that the three sets of
pips, taken anywhere, shall add up
alike on the left side and on the right.
Such a column has been started in the
diagram. It will be seen that the top
three add up to 9 on both sides, the
next three add up to 7 on both sides,
and so on. This is merely an example,
so you can start afresh if you like.
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- ARRANGING THE DOMINOES
Somebody reminded Professor Rackbrane one morning at the breakfast
table that he had promised to tell them in how many different ways the set of
twenty-eight dominoes may be arranged in a straight line, in accordance with
the original rule of the game, left to right and right to left, in any arrangement
counting as different ways. Later on he told them that the answer was
7,959,229,931,520 different ways. He said that it was an exceedingly difficult
problem.
He then proposed that they should themselves find out in how many
different ways the fifteen smaller dominoes (after discarding all those bearing
a 5 or a 6) may similarly be arranged in a line. Of course, you always place
1 against 1, 6 against 6, and so on, the two directions counting different.