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Topic: How many possible connect 4 games are there? (Read 12573 times) |
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marsh8472
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How many possible connect 4 games are there?
« on: Sep 20th, 2012, 12:52am » |
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How many possible combinations of connect 4 games are there?
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marsh8472
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Re: How many possible connect 4 games are there?
« Reply #1 on: Sep 20th, 2012, 8:00am » |
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I wrote something that's cycling through every possible game and counting each one. Is that a feasible way to do this or would it take too long?
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towr
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Re: How many possible connect 4 games are there?
« Reply #2 on: Sep 20th, 2012, 8:54am » |
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I think it's probably doable.
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marsh8472
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Re: How many possible connect 4 games are there?
« Reply #3 on: Sep 20th, 2012, 9:59pm » |
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I have 2.6 billion counted so far but looks like it's barely scratching the surface based on where it is.
From the looks of http://mathworld.wolfram.com/Connect-Four.html it's probably well over 10 trillion
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towr
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Re: How many possible connect 4 games are there?
« Reply #4 on: Sep 20th, 2012, 10:25pm » |
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American trillions (1012), or European trillions (1018)?
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marsh8472
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Re: How many possible connect 4 games are there?
« Reply #5 on: Sep 20th, 2012, 10:55pm » |
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on Sep 20th, 2012, 10:25pm, towr wrote:| American trillions (1012), or European trillions (1018)? |
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American but their numbers are probably counting games that probably are invalid. I wrote the counter in vb maybe I'll write one in another language that can go through them faster 
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marsh8472
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Re: How many possible connect 4 games are there?
« Reply #6 on: Sep 21st, 2012, 6:07am » |
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I think http://www.connectfour.net/Files/connect4.pdf has the answer (it's on the last page). Total combinations is: 70,728,639,995,483.
My program's still counting them. It's at 4 billion right now. I would probably have to leave it running for a few decades at this rate so I'll just take their word for it and quit that
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towr
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Re: How many possible connect 4 games are there?
« Reply #7 on: Sep 21st, 2012, 7:07am » |
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Yeah, you probably need a smarter approach to count the games then just brute-force it.
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Grimbal
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Re: How many possible connect 4 games are there?
« Reply #8 on: Oct 12th, 2012, 1:46am » |
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Even with brute force, it is worth waiting now and run it on a faster computer later.
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skyrnin
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Re: How many possible connect 4 games are there?
« Reply #9 on: Apr 2nd, 2013, 2:43pm » |
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There are many combinations for this game.. cant count.. 
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scottlouie
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Re: How many possible connect 4 games are there?
« Reply #10 on: May 10th, 2013, 3:03am » |
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The number of possible Connect-Four game situations after n plies (n turns) is tabulated at OEISA212693. The total is 4531985219092. More in-depth explanation can be found at the links provided by the OEIS site.
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