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Subject: Re: Who knows the answer of this:

Author: David Hanley

Date: 16:28:51 12/19/01

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On December 19, 2001 at 16:57:46, Michel Langeveld wrote:

>Problem = 1 - ( 16777216! / (16746008! * 16777216 ^ 31208) )

Well, let's see.

16777216! / 16746008! = 16777216 * 16777215 * 16777214 * ..... * 16746009

Because the rest of the factorial cancels out--see?

So, we need to divide that by 16777216 ^ 31208

16777216 * 16777215 * 16777214 * ..... * 16746009
--------------------------------------------------
16777216 ^ 31208

Now, i notice the number of terms in the top is equal to the number of terms in
the bottom, once you expand the exponent, but except the first term, the bottom
terms are larger, in an increasing fashion.  Therefore, the bottom will dominate
the top, making the whole fraction very very tiny.. See:

16777216 * 16777215 * 16777214 * ..... * 16746009
--------------------------------------------------
16777216 * 16777216 * 16777216 * ..... * 16777216

which is like:

16777216   16777215   16777214   .....   16746009
-------- * -------- * -------- * ----- * --------
16777216   16777216   16777216   .....   16777216


A lot of the fractions are close to one, but when you multiply them all out,
they're very very nearly zero.

so 1 - fraction will be very nearly one.


dave



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