def construct_tri(balls)
  #not aware of an easy way to turn linear coordinates into triangular
  #coordinates, so this is all hardcoded for now
  balls[5] = (balls[0]-balls[1]).abs
  balls[6] = (balls[1] - balls[2]).abs
  balls[7] = (balls[2] - balls[3]).abs
  balls[8] = (balls[3] - balls[4]).abs
  balls[9] = (balls[5] - balls[6]).abs
  balls[10] = (balls[6] - balls[7]).abs
  balls[11] = (balls[7] - balls[8]).abs
  balls[12] = (balls[9] - balls[10]).abs
  balls[13] = (balls[10] - balls[11]).abs
  balls[14] = (balls[12] - balls[13]).abs
end

def valid_tri?(balls)
  used = []
  balls.each do |ball|
    return false if used.include?(ball)
    used.push(ball)
  end
  true
end

balls = Array.new

max = 15**5
for i in 0...max
  val = i
  for k in 0...5
    balls[k] = val%15 + 1
    val /= 15
  end
  construct_tri(balls)
  print balls, "\n" if valid_tri?(balls)
end