Determine the largest 3  digit prime factor of 2000 C 1000.
n C r denotes the number of combinations of n things taking r at a time.
661.
Not as elegant as K.S.'s but it follows that 2000!/(1000! * 1000!) is
(2000 * 1999 * 1998 * . . . * 1001 )
(1000 * 999 * 998 * . . . *1)
All the numbers between 1001 and 2000 that are divisible by 2 can be tossed. This leaves numbers between 1001 and 2000 that are divisible by 3 (666, 665, 664 . . .). The highest prime in this set is 661.
Edited on May 12, 2006, 12:45 pm

Posted by Leming
on 20060512 12:37:31 