combinations.rb

#!/bin/ruby

# Attempt to do an imperical proof of my answer to the following homework question:
#
#   Find the number of ways in which seven different toys can be given to three children,
#   if the youngest is to receive three toys, and the others receive two toys each.
#

require 'set'

toys = [:a, :b, :c, :d, :e, :f, :g]
puts "Here are all the toys: #{toys}"

kids = {:summer => 3, :grace => 2, :isabelle => 2}
puts "Here are the kids and how many toys they can have: #{kids}"

allocations = Set.new
got_to_210_at = nil

# Lets repeat the following block a lot (this is a loop)
(1..2000).each do |i|

  # How many combinations have we found already?
  found = allocations.size

  # First we get a randomised ordering of the toys
  shuffled_toys = toys.sample(7)

  # Then we divvy them up 3 for summer, 2 for grace, 2 for isabelle
  # We are using a Set to for each child's collection as ordering is
  # unimportant. ie [:a, :b, :c] is equal to [:b, :c, :a]
  new_lot = {
    :summer   => Set.new(shuffled_toys[0..2]),
    :grace    => Set.new(shuffled_toys[3..4]),
    :isabelle => Set.new(shuffled_toys[5..6]),
  }

  # Finall we add this new distribution to the allocation set
  # If this exact combination (distribution) already exists in the
  # allocations set then it will not be added again, cause it's a set
  # and sets can't have two members that are the same
  allocations.add new_lot


  # Output a summary of where we are at:
  print "Iteration: #{i} "
  print "New Allocation: #{shuffled_toys} - #{allocations.size}" unless found == allocations.size
  puts

  # How many iterations did it take to get to find 210 allocations?
  unless got_to_210_at and allocations.size == 210
    got_to_210_at = i
  end

end

puts "Hit 210 unique allocations after #{got_to_210_at} iterations"