20 ARITHMETICAL RECREATIONS [CH. I 



marked 3, three marked 2, and three marked 1. They play 

 alternately ; A begins by playing one of his cards ; then B plays 

 one of his, and so on. He wins who first plays a card which 

 makes the sum of the points or numbers on all the cards 

 played exactly equal to 50, but he loses if he plays a card 

 which makes this sum exceed 50. The game can be played 

 by noting the numbers on a piece of paper, and it is not 

 necessary to use cards. 



Thus suppose they play as follows. A takes a 4, and scores 4; 

 B takes a 3, and scores 7; A takes a 1, and scores 8; B takes a 6, 

 and scores 14; A takes a 3, and scores 17; B takes a 4, and scores 

 21 ; A takes a 4, and scores 25 ; B takes a 5, and scores 30 ; A 

 takes a 4, and scores 34 ; B takes a 4, and scores 38 ; A takes a 



5, and scores 43. B can now win, for he may safely play 3, 

 since A has not another 4 wherewith to follow it; and if A 

 plays less than 4, B will win the next time. Again, suppose 

 they play thus. .4,6; B, 3 ; A, 1 ; B, 6 ; A, 3 ; B, 4 ; A, 2 ; 

 B, 5; A, 1; B, 5; A, 2; B, 5; A, 2; B, 3. A is now forced to 

 play 1, and B wins by playing 1. 



A slightly different form of the game has also been sug- 

 gested. In this there are put on the table an agreed number 

 of cards, say, for example, the four aces, twos, threes, fours, fives, 

 and sixes of a pack of cards — twenty-four cards in all. Each 

 player in turn takes a card. The score at any time is the sum 

 of the pips on all the cards taken, whether by A or B. He 

 wins who first selects a card which makes the score equal, say, 

 to 50, and a player who is forced to go beyond 50 loses. 



Thus, suppose they play as follows. A takes a 6, and scores 

 6; B takes a 2, and scores 8; A takes a 5, and scores 13; 

 B takes a 2, and scores 15; A takes a 5, and scores 20; B 

 takes a 2, and scores 22 ; A takes a 5, and scores 27 ; B takes 

 a 2, and scores 29; A takes a 5, and scores 34; B takes a 



6, and scores 40 ; A takes a 1, and scores 41 ; B takes a 4, and 

 scores 45 ; J. takes a 3, and scores 48 ; B now must take 1, and 

 thus score 49 ; and A takes a 1, and wins. 



In these variations the object of each player is to get to 

 one of the key numbers, provided there are sufficient available 



