🚀 go-pugleaf

In article <487ou8$bv2@news-s01.ny.us.ibm.net>,
Graham Fletcher <hccnslt@ibm.net> wrote:
>It's been a while since my university days.  Can anyone explain what a 
>Sub-factorial is?  The notation is !4 and apparently !4=9.  I know 4!=24 
>and all but what the heck is !4?  The term was used on a math quiz 
>question given on the Discovery Channel Canada on using three fours and 
>all of the standard operators to construct the numbers from 1 to 16.  In 
>order to construct the numbers above 16, you need to use 4! and !4, but 
>no one explained what !4 is, they just gave the value, 9.
>

I asked the same question on sci.math and got the following answer:

From John P Lawrence <jpl@stat.mps.ohio-state.edu>

It's the number of permutations of n objects such that none of the
objects
are unchanged. A formula for it is n! sum (-1)^k/k!
where the sum is from k=0 to n.

John

David Buck
dbuck@magi.com