THE HAT PUZZLE.
(
Moving Counter Problem)
Ten hats were hung on pegs as shown in the illustration--five silk hats
and five felt "bowlers," alternately silk and felt. The two pegs at the
end of the row were empty.
The puzzle is to remove two contiguous hats to the vacant pegs, then two
other adjoining hats to the pegs now unoccupied, and so on until five
pairs have been moved and the hats again hang in an unbroken row, but
with all the silk ones together and all the felt hats together.
Remember, the two hats removed must always be contiguous ones, and you
must take one in each hand and place them on their new pegs without
reversing their relative position. You are not allowed to cross your
hands, nor to hang up one at a time.
Can you solve this old puzzle, which I give as introductory to the next?
Try it with counters of two colours or with coins, and remember that the
two empty pegs must be left at one end of the row.
Answer:
[Illustration:
1 2 3 4 5 6 7 8 9 10 11 12
+--+--+--+--+--+--+--+--+--+--+--+--+
| | o| | O| | O| | O| | O| | |
+--+--+--+--+--+--+--+--+--+--+--+--+
| | | | O| | O| | O| | O| O| |
+--+--+--+--+--+--+--+--+--+--+--+--+
| | | O| O| | O| | | | O| O| |
+--+--+--+--+--+--+--+--+--+--+--+--+
| | | O| | | O| O| | | O| O| |
+--+--+--+--+--+--+--+--+--+--+--+--+
| | | O| O| O| O| O| | | | | |
+--+--+--+--+--+--+--+--+--+--+--+--+
| | | O| O| O| O| O| | | | | |
+--+--+--+--+--+--+--+--+--+--+--+--+
]
I suggested that the reader should try this puzzle with counters, so I
give my solution in that form. The silk hats are represented by black
counters and the felt hats by white counters. The first row shows the
hats in their original positions, and then each successive row shows how
they appear after one of the five manipulations. It will thus be seen
that we first move hats 2 and 3, then 7 and 8, then 4 and 5, then 10 and
11, and, finally, 1 and 2, leaving the four silk hats together, the four
felt hats together, and the two vacant pegs at one end of the row. The
first three pairs moved are dissimilar hats, the last two pairs being
similar. There are other ways of solving the puzzle.
Informational
