Connect 4 - Number of Winning Arrangements
Date: 6/20/96 at 8:55:40 From: Holy Family School Subject: Connect 4 - Number of Winning Arrangements Can you help us find the formula for the number of winning lines on a 7 x 6 Connect 4 board? Any clues that can point us in the right direction will be most useful.
Date: 6/20/96 at 21:41:50 From: Doctor Chaos Subject: Re: Connect 4 - Number of Winning Arrangements If I understand your question, you are looking for the number of ways you can get "4 in a row", horizontally, vertically, and diagonally. I don't know if there is a "formula" for this but you can definitely explore the patterns on a 6x7 grid. Here's how to start: Look at how many times "4 in a row" fits in ONE ROW OF 6. I see 3 Since there are 7 of these rows, that gives you 21 possibilities. Now move on to the number of times you can fit 4 "4 in a row" in a column of 7. I see 4. With 6 of these columns, you get 24 possibilities. Follow the SAME idea with the diagonals slanting to the RIGHT and the LEFT, and you'll probably come up with the same total I did: 69 Try it! You can also develop your own "formula", by setting up grids of various sizes in a sequence to see if a real pattern emerges. It can be a fun investigation. If you find a "formula" that works, let us know! -Doctor Chaos, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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