I first heard about Project Euler last week on the stackoverflow podcast. Michael Pryor (fogcreek co-founder) makes a quick side reference in discussion with Joel Spolsky, Jeff Atwood and the rest of the SO team. Well I checked it out last week, got hooked and spent most of the weekend earning my "level 1" badge;-)

Aside from dusting off some long-forgotten and arcane knowledge from my youth, I found it a fantastic opportunity to stretch my fundamental ruby chops. In fact, I'd recommend a few questions at Project Euler as a right-of-passage whenever you are learning a new programming language.

I've only been using ruby for a year or so, and in that time thought I had picked up a fair bit. But I was still able to amaze myself at just how many of the problems were knocked over in just 1 or 2 lines with a bit of duck punching and liberal use of blocks with Enumerables. I'm late to the Project Euler craze, so you will already find many people posting hints for specific questions if you just google. I thought I'd share some of the "common code" I've been building up as I go through the questions.

I put a recent copy of the source up on github for anyone who is interested (MyMath.rb), but what follows a sampling of some of the more interesting pieces.

First thing you will note is that I have written all these "common" routines as extensions to some of the fundamental classes in the ruby library: Integer, Array, String.

It doesn't have to be this way, and for less trivial activities you might be right to be concerned about messing with the behaviour of the standard classes. Maybe I'm still enjoying my ruby honeymoon period, but I do get a thrill out of being able to write things like
1551.palindrome?=> true

## Integer Extensions

It's just so easy to code up simple calculation and introspection routines..
class Integer  # @see project euler #15,20,34  def factorial    (2..self).inject(1) { |prod, n| prod * n }  end  # sum of digits in the number, expressed as a decimal  # @see project euler #16, 20  def sum_digits    self.to_s.split('').inject(0) { |memo, c| memo + c.to_i }  end  # num of digits in the number, expressed as a decimal  # @see project euler #25  def num_digits    self.to_s.length  end    # tests if all the base10 digits in the number are odd  # @see project euler #35  def all_digits_odd?    self.to_s.split('').inject(0) { |memo, s| memo + ( s.to_i%2==0 ? 1 : 0 ) } == 0  end    # generates triangle number for this integer  # https://en.wikipedia.org/wiki/Triangle_number  # @see project euler #42  def triangle    self * ( self + 1 ) / 2  endend

Prime numbers feature heavily on Project Euler, and I think calculating a prime series was my first lesson on why you can't brute-force everything;-) Enter the Sieve of Eratosthenes and related goodness..
class Integer   # https://en.wikipedia.org/wiki/Prime_factor  # @see project euler #12  def prime_factors    primes = Array.new    d = 2      n = self          while n > 1     if n%d==0        primes << d        n/=d      else        d+=1      end    end    primes  end    # https://en.wikipedia.org/wiki/Divisor_function  # @see project euler #12  def divisor_count    primes = self.prime_factors    primes.uniq.inject(1) { |memo, p| memo * ( ( primes.find_all {|i| i == p} ).length + 1) }  end    #  # @see project euler #12, 21, 23  def divisors    d = Array.new    (1..self-1).each { |n| d << n if self % n == 0 }    d  end  # @see project euler #  def prime?    divisors.length == 1 # this is a brute force check  end    # prime series up to this limit, using Sieve of Eratosthenes method  # https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes  # @see project euler #7, 10, 35  def prime_series    t = self    limit = Math.sqrt(t)    a = (2..t).to_a    n = 2    while (n < limit) do      x = n*2      begin        a[x-2]=2        x+=n      end until (x > t )      begin        n+=1      end until ( a[n-2] != 2 )    end    a.uniq!  end  # @see project euler #23  def perfect?    self == divisors.sum  end  # @see project euler #23  def deficient?    self > divisors.sum  end  # @see project euler #23  def abundant?    self < divisors.sum  endend

Next we visit the Collatz conjecture and an interesting routine to make numbers "speak english"..
class Integer       # https://en.wikipedia.org/wiki/Collatz_conjecture  # @see project euler #14  def collatz_series    a = Array.new    a << n = self    while n > 1      if n % 2 == 0        n /= 2      else        n = 3*n + 1      end      a << n    end    a    end  # express integer as an english phrase  # @see project euler #17  def speak    case    when self <20      ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten",       "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen" ][self]    when self > 19 && self < 100       a = ["twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"][self / 10 - 2]      r = self % 10      if r == 0        a      else        a + "-" + r.speak      end    when self > 99 && self < 1000      a = (self / 100).speak + " hundred"      r = self % 100      if r == 0        a      else        a + " and " + r.speak      end          when self > 999 && self < 10000      a = (self / 1000).speak + " thousand"      r = self % 1000      if r == 0        a      else        a + ( r <100 ? " and " : " " ) + r.speak      end          else      self    end  endend

Calculating integer partitions is one of my favourites ... a nice, super-fast recursive algorithm. For problems like "how many ways to make \$2 in change?"
class Integer   # calculates integer partitions for given number using array of elements   # https://en.wikipedia.org/wiki/Integer_partition  # @see project euler #31  def integer_partitions(pArray, p=0)    if p==pArray.length-1      1    else      self >= 0 ? (self - pArray[p]).integer_partitions(pArray ,p) + self.integer_partitions(pArray,p+1) : 0    end  end   end

Finally, rotations and palindromes (base 2 or 10): methods that rely on some underlying String routines that come later...
class Integer   # returns an array of all the base10 digit rotations of the number  # @see project euler #35  def rotations    self.to_s.rotations.collect { |s| s.to_i }  end  # @see project euler #4, 36, 91  def palindrome?(base = 10)    case base     when 2      sprintf("%0b",self).palindrome?    else      self.to_s.palindrome?    end  endend

## Array Manipulations

Array handling is particularly important. Start with some simple helpers, then move onto greatest common factor and a couple of least-common multiple implementations. My favourite here - lexicographic permutations.
class Array  # sum elements in the array  def sum    self.inject(0) { |sum, n| sum + n }  end    # sum of squares for elements in the array  # @see project euler #6  def sum_of_squares    self.inject(0) { |sos, n| sos + n**2 }  end    # @see project euler #17  def square_of_sum    ( self.inject(0) { |sum, n| sum + n } ) ** 2  end      # index of the smallest item in the array  def index_of_smallest    value, index  = self.first, 0    self.each_with_index {| obj, i | value, index = obj, i if obj<value  }    index  end  # removes numbers from the array that are factors of other elements in the array  # @see project euler #5  def remove_factors    a=Array.new    self.each do | x |       a << x if 0 == ( self.inject(0) { | memo, y | memo + (x!=y && y%x==0 ? 1 : 0)  } )    end    a  end  # http://utilitymill.com/edit/GCF_and_LCM_Calculator  # @see project euler #5  def GCF    t_val = self    for cnt in 0...self.length-1      num1 = t_val      num2 = self[cnt+1]      num1,num2=num2,num1 if num1 < num2      while num1 - num2 > 0        num3 = num1 - num2         num1 = [num2,num3].max        num2 = [num2,num3].min      end      t_val = num1    end    t_val  end  # http://utilitymill.com/edit/GCF_and_LCM_Calculator  # @see project euler #5  def LCM    a=self.remove_factors    t_val = a    for cnt in 0...a.length-1      num1 = t_val      num2 = a[cnt+1]      tmp = [num1,num2].GCF      t_val = tmp * num1/tmp * num2/tmp    end    t_val    end  # brute force method:  # http://www.cut-the-knot.org/Curriculum/Arithmetic/LCM.shtml  # @see project euler #5  def lcm2    a=self.remove_factors    c=a.dup    while c.uniq.length>1      index  = c.index_of_smallest        c[index]+=a[index]    end    c.first  end  # returns the kth Lexicographical permutation of the elements in the array  # https://en.wikipedia.org/wiki/Permutation#Lexicographical_order_generation  # @see project euler #24  def lexicographic_permutation(k)    k -= 1    s = self.dup    n = s.length    n_less_1_factorial = (n - 1).factorial # compute (n - 1)!        (1..n-1).each do |j|      tempj = (k / n_less_1_factorial) % (n + 1 - j)      s[j-1..j+tempj-1]=s[j+tempj-1,1]+s[j-1..j+tempj-2] unless tempj==0      n_less_1_factorial = n_less_1_factorial / (n- j)    end    s  end    # returns ordered array of all the lexicographic permutations of the elements in the array  # https://en.wikipedia.org/wiki/Permutation#Lexicographical_order_generation  # @see project euler #24  def lexicographic_permutations    a=Array.new    (1..self.length.factorial).each { |i| a << self.lexicographic_permutation(i) }    a  end    end

## String Helpers

Last but not least, some String methods that just make things so much easier...
class String  # sum of digits in the number  # @see project euler #16, 20  def sum_digits    self.split('').inject(0) { |memo, c| memo + c.to_i }  end  # product of digits in the number  # @see project euler #8  def product_digits    self.split('').inject(1) { |memo, c| memo * c.to_i }  end    #  # @see project euler #4, 36, 91  def palindrome?    self==self.reverse  end   # returns an array of all the character rotations of the string  # @see project euler #35  def rotations    s = self    rots = Array[s]    (1..s.length-1).each do |i|      s=s[1..s.length-1]+s[0,1]      rots << s    end    rots   end    end

With all the above in place - and with the aid of a few brain cells - some deceptively complicated questions (like "How many different ways can £2 be made using any number of coins?") are essentially one-liners:
require 'benchmark'require 'MyMath'Benchmark.bm do |r|  r.report {    answer = 200.integer_partitions([200,100,50,20,10,5,2,1])  }end

Love it;-)