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Page started - 12/2/99
Last updated - 20/6/99

Fun

Answer 4: Triangular Billiards

Either 2 florins and a sixpence; or else a half crown and 2 shillings.

Reasoning

Again, Carol's line of argument is presented:

Call them x, y, z; and let x+y+z=s

The chance, that the pocket contains 2 balls, is 2/3; and, if it does, the 'expectation' is the average value of
(y+z), (z+x), (x+y); i.e. it is 2s/3

Also the chance, that it contains only one, is 1/3; and, if it does, the 'expectation' is s/3.

Hence total 'expectation'=4s/9+s/9=5s/9.

Therefore 5s/9=30d.; therefore s=54d=4shillings 6d

Hence, the coins must be 2 florins and a sixpence; or else a half-crown and 2 shillings

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