PLATES AND COINS.
(
Moving Counter Problem)
Place twelve plates, as shown, on a round table, with a penny or orange
in every plate. Start from any plate you like and, always going in one
direction round the table, take up one penny, pass it over two other
pennies, and place it in the next plate. Go on again; take up another
penny and, having passed it over two pennies, place it in a plate; and
so continue your journey. Six coins only are to be removed, and when
these have been placed there should be two coins in each of six plates
and six plates empty. An important point of the puzzle is to go round
the table as few times as possible. It does not matter whether the two
coins passed over are in one or two plates, nor how many empty plates
you pass a coin over. But you must always go in one direction round the
table and end at the point from which you set out. Your hand, that is to
say, goes steadily forward in one direction, without ever moving
backwards.
Answer:
Number the plates from 1 to 12 in the order that the boy is seen to be
going in the illustration. Starting from 1, proceed as follows, where "1
to 4" means that you take the coin from plate No. 1 and transfer it to
plate No. 4: 1 to 4, 5 to 8, 9 to 12, 3 to 6, 7 to 10, 11 to 2, and
complete the last revolution to 1, making three revolutions in all. Or
you can proceed this way: 4 to 7, 8 to 11, 12 to 3, 2 to 5, 6 to 9, 10
to 1. It is easy to solve in four revolutions, but the solutions in
three are more difficult to discover.
This is "The Riddle of the Fishpond" (No. 41, _Canterbury Puzzles_) in a
different dress.
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