may be pardoned for repeating it here: "Place nineteen men outside a yard of nineteen squares, in a figure symmetrical upon the diagonal of the board; such that the men may all be yarded in nineteen moves." Of course, the problem, in this form, is too difficult for a direct attack. It must be solved by reversing it: "Place the nineteen men in a yard, and bring them out into a symmetrical figure in nineteen moves." At first, it is very difficult to get them out at all, in nineteen moves. As you go on, you find more and more of symmetrical figures, into which you can arrange them. One young friend has found nearly eight hundred figures, arising from only three different ways of making the first seven moves. Another player has discovered nearly twenty ways of taking the first seven moves. This seems (in spite of the fact that some of the symmetrical figures are capable of being produced by different modes of approach), to indicate that there are, probably, four or five thousand different figures which fulfill the conditions of the problem. There is, therefore, in this one question, an unlimited amount of amusement, for those who fancy that kind of work, moving the men out and moving them back, in thirty-eight moves.
These problems in chess and in halma are problems of pure. intellectual skill. We chanced, a few months ago, to have had a problem suggested to us, requiring no skill, but depending wholly on chance. Meeting, in a Pullman car, a little Mexican boy, not yet six years old, we were surprised to have him produce a dice box with five little dice and propose to throw for money. When he found us inflexible in refusing, he began to throw for himself, and, keeping an audible account, credited us, in fun, with the alternate throws. We then began to make a memorandum of the number of pips up at each throw of his five dice. Ten throws were equivalent to fifty throws of a single die, and it so happened that his first ten throws gave one hundred and seventy-five pips; the precise theoretical average of fifty throws of a die. It then occurred to us that some persons might find it an interesting solitaire amusement to record a large number of throws made at successive times. The interest would arise in comparing the actual averages of ten consecutive throws, or fifty, or a hundred; and of consecutive tens, fifties, etc., with the theoretical averages. These comparisons might extend from the average of the number of pips up to the number of doublets, triplets, and other special combinations, produced by consecutive throws, or by simultaneous ones. The labor of calculating the chances (how often, for example, with a pair of dice, doublet aces should occur, and how often they should be instantly followed by quatre ace) should be performed by a person in health, and the invalid amuse himself by simply recording a large number of throws, and seeing how
