[amesan]

Chess fans, please help me out.

The problem states: How many unique board positions are possible after 3 moves? The answer given is 5,242. I wrote a little program to solve this, and my answer is 5,362.

Looking out on the web, I could find no postings for this, but there were references to the number after 4 moves. This answer, found on many pages, is 72,084. I ran my program for 4 moves and came up with 72,171.

According to worldchessnetwork.com: in 1895, C. Flye St. Marie calculated that 71,852 positions were possible. Then in 1946, Thomas Dawson added 232 possible en passant captures, bringing the total number of different positions to 72,084.

I don't know what number is correct. I do not see how en passant can come into play after only 4 moves so I question the 72,084 answer. In the analysis accompanying the 5,242 answer, I think there is a flaw in two of the counts. Thus, I still like 5,362.

So, what is the answer for 3 and 4 moves?

[Dark Mind]

I'm personally not that into chess but I think if you sent a Private Message to TeleMad he may be able to help you out. He's our "Resident Chess Master" .

[amesan]

For those following this saga, the answer for 3 moves is 5,362, according to Tom Clymer, Director of Academic Competitions for the National Assessment & Testing organization, which posed the question.

This strengthens the case for the correctness of my program for the answer for 4 moves. At this level, granted, only certain people will care. If you are one of them....

[Dark Mind]

I've sent TeleMad a Private Message. Awaiting response.

*Calling TeleMad... TeleMad, come in.

I'm not positive he'll be able to help out or even want to, but he is really a great chess player and should be able to figure something like that out in a jiffy.

Jiffy- The duration of one tick of the computer's system clock. Often one AC cycle time (1/60 second in the US and Canada, 1/50 most other places), but more recently 1/100 sec has become common.

(Confusingly, the term is sometimes also used for a 1-millisecond wall time interval. Even more confusingly, physicists semi-jokingly use "jiffy" to mean the time required for light to travel one foot in a vacuum, which turns out to be close to one *nanosecond*.)

[Dark Mind]

Oh, and by the way...

Welcome, amesan, to our humble home of science. (and chess.)

[TeleMad]

Originally Posted by Dark Mind

I've sent TeleMad a Private Message. Awaiting response.

*Calling TeleMad... TeleMad, come in.

Been too busy to post on the Net.

Dark Mind: I'm not positive he'll be able to help out ...

I don't know the answer and would have to also write a program to figure it out, and amesan already did this and did it right.

PS: I do remember reading years ago that there are more ways to play the first 10 moves of a game of chess than there are stars in the observable universe.

[Dark Mind]

I wouldn't doubt it for a second. And that is why, ladies and gentlemen, I love chess.

You could live to be a thousand years old and still never have played half the number of *possible* games.

[amesan]

The final post for this thread? (We're now into programming rather than chess.)

turns...board positions.....moves...en passant captures

..1.................20.................20
..2...............400................420
..3............5,362.............9,322
..4..........72,171..........207,106
..5........824,972.......5,107,320..........233

I've vaguely thought of going further, but stars in the sky or atoms in the universe seem better comparisons.

Cheers

[Dark Mind]

That may be so, and it would probably be a waste of time and knowledge. It is just a small trivia fact that would be hard to bring up in a normal conversation.

I see you've stolen Buffy's signature, for shame.