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DOMINOES IN PROGRESSION.
(Problems Concerning Games.
It will be seen that I have played six dominoes, in the illustration, in
accordance with the ordinary rules of the game, 4 against 4, 1 against
1, and so on, and yet the sum of the spots on the successive dominoes,
4, 5, 6, 7, 8, 9, are in arithmetical progression; that is, the numbers
taken in order have a common difference of 1. In how many different ways
may we play six dominoes, from an ordinary box of twenty-eight, so that
the numbers on them may lie in arithmetical progression? We must always
play from left to right, and numbers in decreasing arithmetical
progression (such as 9, 8, 7, 6, 5, 4) are not admissible.