Project Euler problem #86 (First Attempt, Naive I know :)

problem-86.rb

=begin
Cuboid room:

* consider all integer up to cuboids: M x M x M
* where M = 100
* a^2 + b^2 = c^2
* c = sqrt(a^2 + b^2)
* shortest path thru cuboid: Math.sqrt( l**2 + (w + h)**2 )
=end

require 'benchmark'
Benchmark.bm do |x|
  x.report do

    m = 1
    count = nil
    loop do
      range = (1..m+=1)
      arr_of_triplets = range.to_a.repeated_combination(3).to_a
      count = 0
      arr_of_triplets.each do |triplets|
        h, w, l = triplets
        shortest_path = Math.sqrt( l**2 + (w + h)**2 )
        if shortest_path % 1 == 0
          count += 1
        end
      end
      break m if count > 1_000_000
    end
    puts m, count
  end

end

So arr_of_triplets = range.to_a.repeated_combination(3).to_a is going to be a big, big, big array -- on the order of billions of elements when m ~1000.

I'd recommend doing

(1...m).each do |h|
  (1...h).each do |w|
    (1...w).each do |l|

It's the same time complexity but uses almost no space.