Problem 61

61.rb

@@ -0,0 +1,147 @@
+def triangle(n)
+  n * (n + 1) / 2
+end
+
+def square(n)
+  n * n
+end
+
+def pentagon(n)
+  n * (3 * n - 1) / 2
+end
+
+def hexagon(n)
+  n * (2 * n - 1)
+end
+
+def heptagon(n)
+  n * (5 * n - 3) / 2
+end
+
+def octagon(n)
+  n * (3 * n - 2)
+end
+
+def prefix(n)
+  n.to_s.slice(0, 2)
+end
+
+def suffix(n)
+  n.to_s.slice(2, 2)
+end
+
+def find_range(range)
+
+  if range[:numbers].length == 6
+    if suffix(range[:next]) == prefix(range[:first])
+      puts range[:numbers].inject(:+)
+    end
+  end
+
+  range_suffix = suffix(range[:next])
+
+  unless range[:used].include?('triangle')
+    unless $triangles[range_suffix].nil?
+      $triangles[range_suffix].each do |value|
+        new_range = {:used => range[:used] + ['triangle'], :numbers => range[:numbers] + [value], :first => range[:first], :next => value}
+        find_range(new_range)
+      end
+    end
+  end
+
+  unless range[:used].include?('square')
+    unless $squares[range_suffix].nil?
+      $squares[range_suffix].each do |value|
+        new_range = {:used => range[:used] + ['square'], :numbers => range[:numbers] + [value], :first => range[:first], :next => value}
+        find_range(new_range)
+      end
+    end
+  end
+
+  unless range[:used].include?('pentagon')
+    unless $pentagons[range_suffix].nil?
+      $pentagons[range_suffix].each do |value|
+        new_range = {:used => range[:used] + ['pentagon'], :numbers => range[:numbers] + [value], :first => range[:first], :next => value}
+        find_range(new_range)
+      end
+    end
+  end
+
+  unless range[:used].include?('hexagon')
+    unless $hexagons[range_suffix].nil?
+      $hexagons[range_suffix].each do |value|
+        new_range = {:used => range[:used] + ['hexagon'], :numbers => range[:numbers] + [value], :first => range[:first], :next => value}
+        find_range(new_range)
+      end
+    end
+  end
+
+  unless range[:used].include?('heptagon')
+    unless $heptagons[range_suffix].nil?
+      $heptagons[range_suffix].each do |value|
+        new_range = {:used => range[:used] + ['heptagon'], :numbers => range[:numbers] + [value], :first => range[:first], :next => value}
+        find_range(new_range)
+      end
+    end
+  end
+end
+
+$triangles = {}
+$squares = {}
+$pentagons = {}
+$hexagons = {}
+$heptagons = {}
+$octagons = []
+
+n = 1
+t = triangle(n)
+s = square(n)
+p = pentagon(n)
+hex = hexagon(n)
+hep = heptagon(n)
+o = octagon(n)
+
+while t <= 9999 do
+
+  if t > 999 && t < 10000
+    $triangles[prefix(t)] = [] if $triangles[prefix(t)].nil?
+    $triangles[prefix(t)] << t
+  end
+
+  if s > 999 && s < 10000
+    $squares[prefix(s)] = [] if $squares[prefix(s)].nil?
+    $squares[prefix(s)] << s 
+  end
+
+  if p > 999 && p < 10000
+    $pentagons[prefix(p)] = [] if $pentagons[prefix(p)].nil?
+    $pentagons[prefix(p)] << p
+  end
+
+  if hex > 999 && hex < 10000
+    $hexagons[prefix(hex)] = [] if $hexagons[prefix(hex)].nil?
+    $hexagons[prefix(hex)] << hex
+  end
+
+  if hep > 999 && hep < 10000
+    $heptagons[prefix(hep)] = [] if $heptagons[prefix(hep)].nil?
+    $heptagons[prefix(hep)] << hep
+  end
+
+  if o > 999 && o < 10000
+    $octagons << o
+  end
+
+  n += 1
+  t = triangle(n)
+  s = square(n)
+  p = pentagon(n)
+  hex = hexagon(n)
+  hep = heptagon(n)
+  o = octagon(n)
+end
+
+$octagons.each do |o|
+  range = {:used => [], :numbers => [o], :first => o, :next => o}
+  find_range(range)
+end