include Math
 
def main
  puts "6 digits"
  check_range((100..999), 1000)
 
  puts "10 digits"
  check_range((10000..99999), 100000)
end
 
def check_range(r, w)
  s = 0
  r.each do |x|
    org = get_org(x, w)
    if org != 0
      puts "matched: #{org}"
      s = s + org
    end
  end
  puts "sum: #{s}"
end
 
# check x^2+y^2==xxyy and returns original number or 0
def get_org(x, w)
  a = x * (w - x)
  y = sqrt(a).to_i + 1
  if a == y * (y - 1)
    return x * w + y
  else
    return 0
  end
end
 
main
 

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