def generate_pythagorean_triples(upper_bound)
  list_of_triples = []
  a = 2
  b = 3
  while a < upper_bound
    b = a + 1
    while b < upper_bound
      c = Math.sqrt(a**2 + b**2)
      list_of_triples << [a, b, c.to_i] if c % 1 == 0 #this is a check that the sqrt is an integer
      b += 1
    end
    a += 1
  end
  list_of_triples
end

def sums_of_triples(list_of_triples)
  hash_of_sums = {}
  list_of_triples.each do |triple|
    hash_of_sums[triple] = triple.inject(:+)
  end
  hash_of_sums
end

def find_pythagorean_sum(upper_bound, sum_to_match)
  hash_of_sums = sums_of_triples(generate_pythagorean_triples(upper_bound))
  hash_of_sums.detect { |key, value| value == sum_to_match }
end

puts find_pythagorean_sum(500, 1000).first.inject(:*)