You start with a zero and try to reach exactly 100 in 4 stages, each stage consisting of either increasing or decreasing your current number by a factorial n!( number like 1,2,6,24,120,720 etc) .
How many sequences exist to accomplish this task?

Assuming we can use the same factorial more than once, we could have 2! + 2! + 5! - 4!    (2+2+120-24) = 100.  Now, to look for more. 

Posted by ed bottemiller on 2010-03-24 10:56:11