Frogs & Lilypads

Six frogs are sitting on seven lilypads (as shown in the diagram below). Three of the frogs are green and three are blue. The green frogs wish to trade places with the blue frogs. They must be careful not to fall into the water while they trade places.

RULES:

1. One frog at a time may hop onto an empty lilypad or hop over exactly ONE frog of the opposite color onto an empty lilypad.
2. Frogs can only hop forward, never backwards, and never over a frog of the same color.

Determine the pattern to help the frogs trade places. Begin with a simpler problem of one frog on each side (three lily pads). Find the formula to predict how many moves for n frogs on each side.

#of frogs on each side
# of moves to switch sides
Pattern
1
   
   
2
   
   
3
   
   
4
   
   
:
:
   
   
n
   
   

What is counterintuitive about this problem?

What patterns are made by the moves by color?