task is to move all the reds from the left to the right and all the blacks from the right to the left. The middlebox is empty to allow moves.
The moves follow strict rules.
Rule # 1: the reds can only move to the right and the blacks can only move to the left. No backward moves are allowed
Rule # 2: Equally applicable to the black and the reds, each dot can only move one step forward in the box in front of it is empty, and can skip the contiguous box is occupied by a different colored dot to the following box if empty.
While moving your pieces, carefully record all the moves you made. Start first with the 5-boxes set, then the 7-boxes set
Try the same rules for a 9-boxes set and then for an 11-boxes set. Record all your moves on paper
Examine all four cases and find a pattern that relates the number of moves to the number of dots. Explain how you arrived at this conclusion
Create a general formula that will give the number of moves based on the number of dots regardless of how many dots you have.