Six pennies are arranged in the pattern of O's below.

    O O O
   O O O

Nearby pennies are touching. By the fewest number of legal moves, transform the pattern into the pattern

O O O O O O

consecutive pennies touching. A legal move consists of sliding a penny, not picking up a penny, without disturbing the other pennies, to a new position touching at least two pennies. (You might want to look up Moving Quarters for a similar problem with the same rules.)

I played this out in Excel;  I offset cells in consecutive rows as either left or right alignment to simulate the triangular structure.

The first group represents the original layout.  Subsequent ones are the stages as I played it.  [After discussions of layout, I trust that the layout appears as I see it before me prior to post.  Anyway, readers should have little difficulty in understanding my strategy. 
Note Charley has suggested that the solution might be at least 6 moves, can it be done in less than 7?]

   A B C
  D E F

     B C
  D E F A

     B C E
  D   F A

     B   E
  D   F A C

     B   E A
  D   F   C

         E A
  D   F   C B

           A
  D E F   C B

  D E F A C B

(7 MOVES)

Posted by brianjn on 2005-06-05 09:09:42