Problem 76

076.rb

@@ -0,0 +1,29 @@
+require 'pp'
+
+def possibilities(decomposition)
+  if decomposition.size > 2
+    combinations = decomposition.combination(2).to_a.uniq
+    combinations.each do |c|
+      composition = decomposition.clone
+      composition.delete_at(composition.index(c[0]))
+      composition.delete_at(composition.index(c[1]))
+      composition << (c[0] + c[1])
+      composition_string = composition.sort.join
+      unless $found[composition_string]
+        $found[composition_string] = true
+        possibilities(composition)
+      end
+    end
+  end
+end
+
+answers = []
+3.upto(15) do |target|
+  decomposition = Array.new(target) { 1 }
+  $found = {decomposition.join => true}
+
+  start_time = Time.now
+  possibilities(decomposition)
+  answers << $found.size
+end
+pp answers.join(',')