Line Sort
Pennies are laid out on a line of spaces always starting with a row of heads and a row of tails
separated by one blank space. There are always an equal number of heads and tails. You may
move the pennies either by sliding any penny one space in either direction, or by jumping over
any one adjacent penny onto a blank space. Only one penny is allowed to occupy any given
space at any one time. Your goal is to exchange the places of the heads and the tails in as few
moves as possible.
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What is the least number of moves that it will take for one head and one tail to exchange
places?
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What is the least number of moves that it will take for two heads and two tails to exchange
places?
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What is the least number of moves that it will take for three heads and three tails to exchange
places?
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How can you know that you have found a way to do this in the least number of moves?
Is there any pattern or system in the way that you are moving the coins?
Determine how many moves it would take for any larger number of heads and tails to
exchange places in this game.