- #1
NickBach
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There's a game that's been around for a long time called Connect 4. It is a 2-player game consisting of 7 columns that can hold 6 discs each. The players alternate dropping a disc of their color into one of the 7 columns until a player has 4 in a row, either horizontally, vertically, or in a diagonol (or until all 42 spots are filled in without a 4-in-a-row sequence resulting that is a tie). I'm trying to determine how many different possible sequences of moves can be made to fill in the remaining spots (assuming a tie will result) at any point during the game. For example, assume the 7 colums already have 2, 1, 6, 4, 5, 0, 2 discs in them (a total of 20), how many ways can the last 22 positions be filled in? Remember, all 22 remaining spots cannot be selected for the next move, only the next one up in each column that currently has less than 6 discs in them. And also, if player A drops 2 discs into the 1st column while player B drops 1 disc into the 4th and then the 5th columns, it should be considered a different sequence than if player B first dropped a disc into the 5th column followed by a disc into the 4th column on this second turn.
Thanks,
Nick
Thanks,
Nick