# Amusements in Mathematics HTML version

Problems Concerning Games
"The little pleasure of the game."
MATTHEW PRIOR.
Every game lends itself to the propounding of a variety of puzzles. They can be made, as
we have seen, out of the chessboard and the peculiar moves of the chess pieces. I will
now give just a few examples of puzzles with playing cards and dominoes, and also go
out of doors and consider one or two little posers in the cricket field, at the football
match, and the horse race and motor-car race.
378.—DOMINOES IN PROGRESSION.
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
379.—THE FIVE DOMINOES.
Here is a new little puzzle that is not difficult, but will probably be found entertaining by
my readers. It will be seen that the five dominoes are so arranged in proper sequence (that
is, with 1 against 1, 2 against 2, and so on), that the total number of pips on the two end
dominoes is five, and the sum of the pips on the three dominoes in the middle is also five.
There are just three other arrangements giving five for the additions. They are: —
(1—0) (0—0) (0—2) (2—1) (1—3)
(4—0) (0—0) (0—2) (2—1) (1—0)
(2—0) (0—0) (0—1) (1—3) (3—0)
Now, how many similar arrangements are there of five dominoes that shall give six