Re: Chess boards & connections.

In article <1145569228.272184.92380@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, dynamics writes:
Michael Stemper wrote:
In article <1145555339.841442.203250@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, dynamics writes:
Trying to calculate if I can write a Chess AI.

I need to define all possible boards.

providing 64*65=4160 boards.

Nope.

Place the first of the 64 pieces. How many choices for a square do
you have? 65. Now, for each of those possibilities, you have 64 choices
for placing the second piece. So, two pieces already uses up your 4160
boards. If you place a third piece, you'll have 63 available squares
for each of those 4160 possibilities, or 65*64*63 = 262080. To place
64 pieces on 65 squares -- even with disallowing two pieces on the same
square from the start -- you're going to have 65! possible boards.

As Proginoskes pointed out elsewhere, this number (65!) is actually
low. According to:
<http://www.scottaaronson.com/writings/bignumbers.html>
there are about 10^50 possible boards.

You are too complicated. All I needed was the 2D Array
I defined by matrix (64,65) defining all boards.

That only gives you 4160 boards, or about one out of every
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

(I'll skip using exclusion right now, like two pieces
can't occupy the same square, but all that means
is there are < 4160 possible boards).

Nope. Like I pointed out above, even if you build in "exclusion" from
the start, you'll need to add a lot of zeros to the right of "4160"

Well then provide the needed Array,

I gave you an estimate as to its size: about 10^50.

I'll repeat
I get a (64,65) for ALL configurations, including
many that are impossible.

Repeating it doesn't make it true.

--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.



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