THE HORSE-RACE PUZZLE.
(
Problems Concerning Games.)
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 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."
Answer:
The answer is: L12 on Acorn, L15 on Bluebottle, L20 on Capsule.
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