Three horses--Acorn, Bluebottle, and Capsule--start in a race. The odds are 4 to 1, Acorn; 3 to 1, Bluebottle; 2 to 1, Capsule. Now, how much must I invest on each horse in order to win L13, no matter which horse comes in first? Supposing, as an example, that I betted L5 on each horse. Then, if Acorn won, I should receive L20 (four times L5), and have to pay L5 each for the other two horses; thereby winning L10. But it will be found that if Bluebottle was first I should only win L5, and if Capsule won I should gain nothing and lose nothing. This will make the question perfectly clear to the novice, who, like myself, is not interested in the calling of the fraternity who profess to be engaged in the noble task of "improving the breed of horses." 391.--THE MOTOR-CAR RACE. Sometimes a quite simple statement of fact, if worded in an unfamiliar manner, will cause considerable perplexity. Here is an example, and it will doubtless puzzle some of my more youthful readers just a little. I happened to be at a motor-car race at Brooklands, when one spectator said to another, while a number of cars were whirling round and round the circular track:-- "There's Gogglesmith--that man in the white car!" "Yes, I see," was the reply; "but how many cars are running in this race?" Then came this curious rejoinder:-- "One-third of the cars in front of Gogglesmith added to three-quarters of those behind him will give you the answer." Now, can you tell how many cars were running in the race? PUZZLE GAMES. "He that is beaten may be said To lie in honour's truckle bed." HUDIBRAS. It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual. For example, if it were possible for us so to master the complexities of the game of chess that we could be assured of always winning with the first or second move, as the case might be, or of always drawing, then it would cease to be a game and would become a puzzle. Of course among the young and uninformed, when the correct winning play is not understood, a puzzle may well make a very good game. Thus there is no doubt children will continue to play "Noughts and Crosses," though I have shown (No. 109, "_Canterbury Puzzles_") that between two players who both thoroughly understand the play, every game should be drawn. Neither player could ever win except through the blundering of his opponent. But I am writing from the point of view of the student of these things. The examples that I give in this class are apparently games, but, since I show in every case how one player may win if he only play correctly, they are in reality puzzles. Their interest, therefore, lies in attempting to discover the leading method of play. 392.--THE PEBBLE GAME.