fixed some old code + added solutions for new problems

euler001.rb

@@ -0,0 +1,9 @@
+def multiples_of_three_and_five_below(n)
+  multiples = []
+  (3..n-1).each do |i|
+    multiples << i if ((i % 3 == 0) || (i % 5 == 0))
+  end
+  multiples
+end
+
+puts multiples_of_three_and_five_below(1000).inject(:+)

euler015.rb

@@ -0,0 +1,16 @@
+def factorial(n)
+  i = 1
+  while (n > 0)
+    i *= n
+    n -= 1
+  end
+  i
+end
+
+def combination(n, k)
+  factorial(n) / (factorial(k) * factorial(n-k))
+end
+
+def lattice_paths(size)
+  combination(2*size, size)
+end

euler026.rb

@@ -0,0 +1,29 @@
+def gcd(a, b)
+  b == 0 ? a : gcd(b, a % b)
+end
+
+def is_relatively_prime?(a, b)
+  gcd(a, b) == 1
+end
+
+def multiplicative_order_of_ten(n)
+  return nil unless is_relatively_prime?(10, n)
+  (2..n-1).each do |i|
+    return i if 10**i % n == 1
+  end
+  return nil
+end
+
+def longest_repeating_decimal
+  highest_order = 0
+  highest_order_n = 0
+  (1..1000).each do |n|
+    order = multiplicative_order_of_ten(n)
+    next if order.nil?
+    if highest_order < order
+      highest_order = order
+      highest_order_n = n
+    end
+  end
+  highest_order_n
+end

euler028.rb

@@ -0,0 +1,17 @@
+def spiral(size)
+  max_value = size**2
+
+  diagonals = [1]
+  diagonal_increase_value = 2
+  current_num = 1
+
+  until current_num == max_value
+    4.times do
+      current_num += diagonal_increase_value
+      diagonals << current_num
+    end
+    diagonal_increase_value += 2
+  end
+
+  diagonals.inject(:+)
+end

euler031.rb

@@ -1,18 +1,20 @@
 def change(n, list_of_coins)
-  changeHelper(n, list_of_coins, [])
+  change_helper(n, list_of_coins, [])
 end
 
-def changeHelper(n, list_of_coins, result_list)
+def change_helper(n, list_of_coins, result_list)
   if list_of_coins.empty?
-    [result_list]
+    return []
   elsif n == 0
-    [result_list]
+    return [result_list]
   else
-    if n >= list_of_coins.first
+    list_of_coins.each do |coin|
-      changeHelper(n - list_of_coins.first, list_of_coins, result_list << list_of_coins.first) +
+      if n < coin
-        changeHelper(n, list_of_coins[1..list_of_coins.count-1], result_list)
+        return []
       else
-      changeHelper(n, list_of_coins[1..list_of_coins.count-1], result_list)
+        return change_helper(n - coin, list_of_coins, result_list + [coin]) + change_helper(n, list_of_coins - [coin], result_list)
       end
     end
+  end
+
 end

euler033.rb

@@ -1,21 +1,56 @@
-class Integer
+def gcd(a, b)
-  def mod_exp(exp, mod)
+  b == 0 ? a : gcd(b, a % b)
-    exp < 0 and raise ArgumentError, "negative exponent"
-    prod = 1
-    base = self % mod
-    until exp.zero?
-      exp.odd? and prod = (prod * base) % mod
-      exp >>= 1
-      base = (base * base) % mod
-    end
-    prod
-  end
 end
 
-PHI = (1 + Math.sqrt(5)) / 2
+def generate_fractional_pairs
-
+  pairs = []
-def fib(n)
+  (10..99).each do |i|
-  ((PHI ** n - (-1 / PHI) ** n) / Math.sqrt(5)).to_i
+    (10..99).each do |j|
+      pairs << [i,j] if i < j
+    end
+  end
+  pairs
 end
 
-puts fib(8)
+def check_weird_cancellations
+  solutions = []
+  fractions = generate_fractional_pairs
+
+  fractions.each do |fraction|
+    next if fraction.first % 10 == 0
+    num = fraction.first.to_s
+    den = fraction.last.to_s
+
+    if (num.include?(den[0]))
+      digit = num[num.index(den[0])]
+      new_num = num.delete(digit)
+      new_den = den.delete(digit)
+    elsif (num.include?(den[1]))
+      digit = num[num.index(den[1])]
+      new_num = num.delete(digit)
+      new_den = den.delete(digit)
+    end
+
+    solutions << [fraction.first, fraction.last] if (num.to_f / den.to_f) == (new_num.to_f / new_den.to_f)
+
+  end
+  solutions
+end
+
+def reduce_fraction(numerator, denominator)
+  until (gcd = gcd(numerator, denominator)) == 1
+    numerator /= gcd
+    denominator /= gcd
+  end
+  [numerator, denominator]
+end
+
+def multiply_fractions(fractions)
+  numerators = 1
+  denominators = 1
+  fractions.each do |fraction|
+    numerators *= fraction.first
+    denominators *= fraction.last
+  end
+  reduce_fraction(numerators, denominators)
+end

euler034.rb

@@ -0,0 +1,17 @@
+def factorial(n)
+  i = 1
+  while (n > 0)
+    i *= n
+    n -= 1
+  end
+  i
+end
+
+def curious_numbers(range)
+  solutions = []
+  (3..range).each do |i|
+    digits = i.to_s.split('').map(&:to_i)
+    solutions << i if digits.map { |x| factorial(x) }.inject(:+) == i
+  end
+  solutions
+end

euler035.rb

@@ -0,0 +1,29 @@
+require 'prime'
+
+def primes_up_to(n)
+  Prime.take_while { |x| x < n }
+end
+
+def integer_rotations(n)
+  rotations = []
+  digits = n.to_s.split('')
+
+  digits.count.times do
+    rotations << digits.join('').to_i
+    digits.rotate!
+  end
+
+  rotations
+end
+
+def is_circular?(n)
+  circular = true
+  integer_rotations(n).each do |perm|
+    return false unless Prime.prime?(perm)
+  end
+  circular
+end
+
+def circular_primes_up_to(n)
+  primes_up_to(n).select { |x| puts x; is_circular?(x) }
+end

euler036.rb

@@ -0,0 +1,11 @@
+def is_palindromic_base_ten?(n)
+  n.to_s == n.to_s.reverse
+end
+
+def is_palindromic_base_two?(n)
+  n.to_s(2) == n.to_s(2).reverse
+end
+
+def palindromic_up_to(n)
+  (1..n).select { |i| is_palindromic_base_two?(i) && is_palindromic_base_ten?(i) }
+end

euler037.rb

@@ -0,0 +1,32 @@
+require 'prime'
+
+def truncate_right(n)
+  n.to_s[0..-2].to_i
+end
+
+def truncate_left(n)
+  n.to_s[1..-1].to_i
+end
+
+def prime_truncatable_right?(n)
+  return false unless Prime.prime?(n)
+  truncated_prime = n
+  until (truncated_prime = truncate_right(truncated_prime)) == 0
+    return false unless Prime.prime?(truncated_prime)
+  end
+  return true
+end
+
+def prime_truncatable_left?(n)
+  return false unless Prime.prime?(n)
+  truncated_prime = n
+  until (truncated_prime = truncate_left(truncated_prime)) == 0
+    return false unless Prime.prime?(truncated_prime)
+  end
+  return true
+end
+
+
+def primes_truncatable_up_to(n)
+  (1..n).select { |i| prime_truncatable_right?(i) && prime_truncatable_left?(i) }
+end