Project Euler

Problem-1.rb

# Find the sum of all the natural multiples of 3 or 5 below 1000.

puts (1...1000).select { |i| i % 3 == 0 or i % 5 == 0 }.inject { |s,i| s+i }

Problem-2.rb

# Find the sum of all the even-valued terms in the fibonacci 
# sequence which do not exceed four million.

require 'rubygems'
require 'memoize'

include Memoize

def fibonacci n
  return n if n < 2
  fibonacci(n-2) + fibonacci(n-1)
end

def last_fib n,b
  return n if fibonacci(n+1) > b
  last_fib(n+1,b)
end

memoize :fibonacci

puts 0.upto(last_fib(0,4e6)).map { |i| fibonacci i }.select { |n| n % 2 == 0 }.inject { |s,i| s+i }

Problem-3.rb

# What is the largest prime factor of the number 600851475143?

require 'mathn'

class Proc
  def << g
    lambda {|*args| self.call(g.call(*args)) }
  end
end

class Integer
  def largest_prime_factor
    first_factor = lambda do |x|
      (2..x).find { |i| x % i == 0 }
    end

    complement = lambda { |a| a / first_factor.call(a) }
    rec = :largest_prime_factor.to_proc << complement

    return first_factor.call(self) if complement.call(self) == 1
    rec.call(self)
  end
end

puts 600851475143.largest_prime_factor
# => 6857

Problem-4.rb

# Find the largest palindrome made from the product of two 3-digit numbers.

BOTTOM = 100**2
TOP = 999**2

class Integer
  def greatest_three_digit_factor
    (100..999).to_a.reverse.find { |x| self % x == 0 }
  end
  
  def three_by_three?
    unless greatest_three_digit_factor.nil?
      (self/greatest_three_digit_factor).to_s.size == 3
    end
  end
end

def greatest_three_by_three_palindrome
  (BOTTOM..TOP).select { |x| x.to_s == x.to_s.reverse and x.three_by_three? }.max
end

puts greatest_three_by_three_palindrome
# => 906609

Problem-5.rb

# What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?