\(l\) players are playing a game of Chain Reaction on a \(m \times n\) 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 \(l, m, \) and \(n\).
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.