Hey, original Tetris proof guy here. Glad to see it works with two lamps! However, since the 'one of each colour' property is a necessary property for a rectangular arrangement to exist, not a sufficient one, simply having the 'same number of colours' doesn't mean that such an arrangement definitely exists. (It's pretty easy to think of an example of a set of pieces where one doesn't, but the property is satisfied).
The fact that an arrangement does exist in the two lamp case is neat though.