Coin Flip

In a row of four squares, place a penny, nickel, dime, quarter - from left to right. The object is to reverse their order - that is, to get them in the sequence quarter, dime, nickel, penny - in the fewest possible turns. In each turn, move a coin one square to the left or right. You may move a coin only into an empty square or onto an adjacent coin of higher value (e.g., a penny can move onto a nickel, but not vice versa.) Only the top coin of a stack may move. What is the smallest number of turns necessary to effect the switch?

Source: Will Shortz, Games Magazine, August 1992. Used as Ken's POTD 9/6/94.

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