A banker had a sporting customer who was always anxious to wager on
anything. Hoping to cure him of his bad habit, he proposed as a wager
that the customer would not be able to divide up the contents of a box
containing only sixpences into an exact number of equal piles of
sixpences. The banker was first to put in one or more sixpences (as many
as he liked); then the customer was to put in one or more (but in his
case not more than a pound in value), neither knowing what the other put
in. Lastly, the customer was to transfer from the banker's counter to
the box as many sixpences as the banker desired him to put in. The
puzzle is to find how many sixpences the banker should first put in and
how many he should ask the customer to transfer, so that he may have the
best chance of winning.