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euler.rb
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euler.rb
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#!/usr/bin/env ruby
# Project Euler in Ruby (1.8.5)
# John Evans <john@jpevans.com>
require 'rational'
# Euler #1
# Answer: 233168
#
# If we list all the natural numbers below 10 that are multiples of 3 or 5,
# we get 3, 5, 6 and 9. The sum of these multiples is 23.
#
# Find the sum of all the multiples of 3 or 5 below 1000.
def euler1
(1..999).select { |n| n % 3 == 0 or n % 5 == 0 }.inject(0) { |a,b| a + b }
end
# Euler #2
# Answer: 4613732
#
# Each new term in the Fibonacci sequence is generated by adding the previous
# two terms. By starting with 1 and 2, the first 10 terms will be:
#
# 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
#
# Find the sum of all the even-valued terms in the sequence which do not
# exceed four million.
def euler2
n, a, b = 2, 1, 2
while true do
c = a + b
if c > 4000000
break
end
if c % 2 == 0
n = n + c
end
a, b = b, c
end
n
end
# Euler #3
# Answer: 6857
#
# The prime factors of 13195 are 5, 7, 13 and 29.
#
# What is the largest prime factor of the number 600851475143 ?
class Fixnum
def prime?
if self == 2
return true
end
(2..(Math.sqrt(self).ceil)).each do |possible_factor|
if self % possible_factor == 0
return false
end
end
return true
end
end
def euler3
target = 600851475143
Math.sqrt(target).ceil.downto(2) do |n|
if target % n == 0 and n.prime?
return n
end
end
end
# Problem #4
# Answer: 906609
#
# A palindromic number reads the same both ways. The largest
# palindrome made from the product of two 2-digit numbers is 9009 =
# 91 99.
#
# Find the largest palindrome made from the product of two 3-digit
# numbers.
class Fixnum
def palindrome?
"#{self}" == "#{self}".reverse
end
end
def euler4
result = 0
(100..999).each do |a|
(100..999).each do |b|
p = a * b
if p > result and p.palindrome?
result = p
end
end
end
result
end
# Problem #5
# Answer: 232792560
#
# 2520 is the smallest number that can be divided by each of the
# numbers from 1 to 10 without any remainder.
#
# What is the smallest number that is evenly divisible by all of the
# numbers from 1 to 20?
def euler5
(1..20).inject(1) { |result, n| result.lcm n }
end
# Problem #6
# Answer: 25164150
#
# The sum of the squares of the first ten natural numbers is,
# 1² + 2² + ... + 10² = 385
# The square of the sum of the first ten natural numbers is,
# (1 + 2 + ... + 10)² = 55² = 3025
# Hence the difference between the sum of the squares of the first
# ten natural numbers and the square of the sum is 3025 - 385 = 2640.
#
# Find the difference between the sum of the squares of the first one
# hundred natural numbers and the square of the sum.
def euler6
sum = sum_of_squares = 0
1.upto(100) do |n|
sum += n
sum_of_squares += n * n
end
(sum * sum) - sum_of_squares
end
# Problem #7
# Answer: 104743
#
# By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
#
# What is the 10001st prime number?
def euler7
n = 2
primes = []
result = 0
while true do
is_prime = true
primes.each do |v|
if n % v == 0 then
is_prime = false
break
end
end
if is_prime then
if primes.length >= 10000 then
result = n
break
end
primes.push(n)
end
n = n + 1
end
result
end
MAX_EULER = 7
if __FILE__ == $0
if ARGV.length > 0
for arg in ARGV
puts "#{arg}: #{eval("euler#{arg}")}"
end
else
1.upto(MAX_EULER) do |n|
puts "#{n}: #{eval("euler#{n}")}"
end
end
end