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"Flipping" Dimes and Pennies


Place two dimes and two pennies in a line with a space between them like this:

 P P   D D
 _ _ _ _ _

Using a sequence of moves, switch the two groups of coins to achieve this position:

 D D   P P
 _ _ _ _ _

Moves are of two types:

  1. slide a coin to an (adjacent) empty space.
  2. jump a coin over another coin into an empty space.

Type (1) move:

 P P D   D
 _ _ _ _ _

Type (2) move:

 P   D P D
 _ _ _ _ _

The underlines show the (only) five legal locations for the coins to occupy.

What is the smallest number of moves needed?

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