Exercise 1 solution

Output (run): gains about [0.79, 1.16, 1.16]
(200, 40, 40)   -> (157, 46, 46)
(100, 100, 100) -> (79, 116, 116)
(120, 120, 120) -> (94, 139, 139)
(80, 80, 80)    -> (63, 93, 93)

The three greys, which were correct to begin with, now lean blue-green (cyan). The large red object made the red average high, so the algorithm turned red down and green and blue up. The gray world assumption (average colour is neutral) fails when the scene is dominated by one colour. This is my illustration; real automatic white balance is more sophisticated (check).