players are playing a game of Chain Reaction on a grid. They start with an empty grid, and then when their turn comes they place on orb on the grid.
Here are two challenging problems:
1) What is the maximum number of moves the game can last?
2) What is the minimum number of moves the game can last?
Answer in terms of and .
Details and assumptions
I haven't solved it, so I don't know the solution. I don't even know if a (nice) solution exists, however it seems like an interesting problem to me and I hope you will like it too. Feel free to use any method(s) to get the answer - pen and paper, marker and whiteboard, programming, Wolfram|Alpha or anything else that you like!
Post below any ideas / strategies that come to your mind that could be used to maximize / minimize the number of moves.