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?

As Charlie has demonstrated, there are 4!/2! [=12] sequences using the tetrad (- 4!, + 2!, + 2!, + 5!); and and 4! [=24] sequences using the tetrad (- 4!, - 2!, + 3!, + 5!) for a total of 36 sequences using a tetrad of factorials.

Thinking outside the box, if n were permitted to be a non-integer, I suspect there are an infinite number of tetrads and, hence, sequences -- but, as I am not that familiar with the gamma function, I can not provide any such examples.

Edited on March 24, 2010, 2:28 pm

Posted by Dej Mar on 2010-03-24 14:26:47