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.

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.

Hint:

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.