You have quarters laid out in the following pattern on the left and you want to move quarters to form the pattern on the right.

  Q      Q Q
 Q Q    Q   Q
Q Q Q    Q Q

Before| |After

The only rule is you must slide a coin without moving any others, such that the coin's ending location touches two other quarters. This means the following moves are illegal:

 A 1     Moving C to 1    
B C D 2  Moving B to 2  
 E F 

What is the shortest solution?

(In reply to re(3): 3 move solution, sorry Carlos, sorry Mindy by Hugo)

Ok, Hugo, I hadn't understood the rule of the moved coin  necessarily touching 2 coins at the end. But on the hipothesis that my first movement were legal, you say there would be a 2 step solution moving D through B and E (I thought it wasn't legal):
        A  C
     B     
  D   E   F

But if that movement you suggest were legal, I think I've got a valid 3 move solution:

       A
    B   C
 D    E    F

    B   C   A
 D    E   F

    B   C
 D    E   F
          A

    B   C
 D         F
    E   A

And Mindy: you're right if a perfectly regular hexagone is required at the end, but that condition was not expressed. But of course it's implied in the shapes given in the formulation of the problem. But I have to say that the deformation in my final hexagone was very small. However, this problem does not exist in the solution I'm suggesting now

Posted by carlos on 2005-11-27 15:50:15