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THE ECCENTRIC CHEESEMONGER.

(Moving Counter Problem)
The cheesemonger depicted in the illustration is an inveterate puzzle
lover. One of his favourite puzzles is the piling of cheeses in his
warehouse, an amusement that he finds good exercise for the body as well
as for the mind. He places sixteen cheeses on the floor in a straight
row and then makes them into four piles, with four cheeses in every
pile, by always passing a cheese over four others. If you use sixteen
counters and number them in order from 1 to 16, then you may place 1 on
6, 11 on 1, 7 on 4, and so on, until there are four in every pile. It
will be seen that it does not matter whether the four passed over are
standing alone or piled; they count just the same, and you can always
carry a cheese in either direction. There are a great many different
ways of doing it in twelve moves, so it makes a good game of "patience"
to try to solve it so that the four piles shall be left in different
stipulated places. For example, try to leave the piles at the extreme
ends of the row, on Nos. 1, 2, 15 and 16; this is quite easy. Then try
to leave three piles together, on Nos. 13, 14, and 15. Then again play
so that they shall be left on Nos. 3, 5, 12, and 14.


Answer:

To leave the three piles at the extreme ends of the rows, the cheeses
may be moved as follows--the numbers refer to the cheeses and not to
their positions in the row: 7-2, 8-7, 9-8, 10-15, 6-10, 5-6, 14-16,
13-14, 12-13, 3-1, 4-3, 11-4. This is probably the easiest solution of
all to find. To get three of the piles on cheeses 13, 14, and 15, play
thus: 9-4, 10-9, 11-10, 6-14, 5-6, 12-15, 8-12, 7-8, 16-5, 3-13, 2-3,
1-2. To leave the piles on cheeses 3, 5, 12, and 14, play thus: 8-3,
9-14, 16-12, 1-5, 10-9, 7-10, 11-8, 2-1, 4-16, 13-2, 6-11, 15-4.










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