Project Euler-Problem 20

Description

From Project Euler:

n! means n x (n - 1) x ... x 3 x 2 x 1

For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!

Solution

The first thing that we need to solve this problem is a quick method for computing factorials. Since Ruby supports arbitrary precision integers, computing 100! will not be too big of a task.

class ::Integer
  def fact
    (1..self).reduce(1, :*)
  end
end

We will also need our digits method from back in Problem 8. With these two things together, we can put together a fairly trivial solution.

100.fact.digits.reduce(0, :+)

The full source and specifications can be seen on github. Next time, evaluating the sum of all amicable pairs under 10,000.