Spotted markers?

Usage examples of dominoes.

We dispense with all those dominoes Pg 84that have a five or a six on them and limit ourselves to the fifteen that remain, where the double-four is the highest.

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.

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?

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.

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.

This is the smallest summation possible with any selection of dominoes from an ordinary box of twenty-eight.

But the puzzle is to make a selection of eighteen dominoes and arrange them (in exactly the form shown) so that the summations shall be 18 in all the fourteen directions mentioned.

You have been over all the lines once only, and by repeating all these figures in this way, 41—13—30—04—42—21—10—02—23—34, you get an arrangement of the dominoes (without the doubles) which will be perfectly clear.

The dominoes may, therefore, be arranged in a circle in just 264 different ways, leaving out the doubles.

You may start with any domino, except the 4—4 and those that bear a 5 or 6, though only certain initial dominoes may be played either way round.

If we used a box of dominoes extending to 9—9, there would be forty different ways.

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.

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.

In the meantime they were playing a game called Spotless Dominoes, in which plain pieces of ivory had to be arranged in certain linear patterns.