Difficulty Level 6: Choose the red box graph # 1. Play with students "HO", "G", "H", "L", the "E" in the second row, "O", "P", and "T". Put some students on the left bank, aiming to the right, and some to the right, aiming to the left. Try to do it with boat size 2.
You will not succeed. Why not? Look at the state graph below (with isolated vertices and edges deleted). You get two isomorphic copies, and corresponding vertices in both parts correspond to states with left and right interchanged.
Research Question: For which game graphs can you never interchange sides, like explained above?
In the example above, you can never interchange sides.
Research Question: Is there a game graph where you may interchange sides for a given start configuration, but where you cannot do it for another?
Challenges,Erich Prisner, 2002-2004