THE PARLOR-GAME CURE. 533 



may be pardoned for repeating it here : " Place nineteen men out- 

 side 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 diffi- 

 cult for a direct attack. It must be solved by reversing it : " Place 

 the nineteen men in a yard, and bring them out into a symmetri- 

 cal 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, prob- 

 ably, four or five thousand different figures which fulfill the con- 

 ditions 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 soli- 

 taire amusement to record a large number of throws made at suc- 

 cessive 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 com- 

 binations, produced by consecutive throws, or by simultaneous 

 ones. The labor of calculating the chances (how often, for ex- 

 ample, with a pair of dice, doublet aces should occur, and how often 

 they should be instantly followed by quatre ace) should be per- 

 formed by a person in health, and the invalid amuse himself by 

 simply recording a large number of throws, and seeing how 



