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?
(In reply to
Gamma a break! (spoiler) by Dej Mar)
As can be seen on Wolfram's Mathworld, the Gamma function is continuous and can provide any value other than zero (you might need to use a negative argument to get really close to zero).
A particular case is Gamma(5.0270504634512...) = 25 so that all four n's could be the same number. In fact, as you can see from the graph of the Gamma function, there are infinitely many arguments that would produce a value of 25, but only two of these arguments are positivethe other being 0.039154537388342....

Posted by Charlie
on 20100324 15:46:52 