[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.