Connect 4 is a solved game with a strategy that will win every time if played perfectly. It's played on a 2-dimensional 7x6 grid, and won if you can connect four (heh) of your pieces in a row.
This can be abstracted to a game trying to connect N pieces on an k-dimensional grid of size <k1, k2, ..., kN>. Is there a name for this generalized Connect 4 game? It's a type of connection game, but I don't see anything like it listed.
The main question on my mind: given a k-dimensional grid of size <k1, ..., kn>, the goal to make a connected path of length N in the grid, and the constraint that you have to "drop" your piece in from the "top" of the grid (not sure what "top" means in dimensions higher than 3), is this game solvable for any N and any grid shape?
