There are no morals in puzzles. When we are solving the old puzzle of the captain who, having to throw half his crew overboard in a storm, arranged to draw lots, but so placed the men that only the Turks were sacrificed, and all the Christians left on board, we do not stop to discuss the questionable morality of the proceeding. And when we are dealing with a measuring problem, in which certain thirsty pilgrims are to make an equitable division of a barrel of beer, we do not object that, as total abstainers, it is against our conscience to have anything to do with intoxicating liquor. Therefore I make no apology for introducing a puzzle that deals with betting.
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 £$13,$ no matter which horse comes in first? Supposing, as an example, that I betted £$5$ on each horse. Then, if Acorn won, I should receive £$20$ (four times £$5$), and have to pay £$5$ each for the other two horses; thereby winning £$10.$ But it will be found that if Bluebottle was first I should only win £$5,$ 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."
Solutions: 1
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