jpeggg

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.

Not surprised. Tried an Apple Watch (Sport) for a week or so before returning it for a refund. I just couldn't really work out what it was good for, apart from delivering notifications to my wrist. I also wasn't particularly impressed by the battery life, I think I'd need 2 days (for days where I didn't have the chance to charge it overnight) to feel confident using it.

Exactly that - it's a proof that in this case a solution can't be found. Having a collection of pieces that doesn't violate the assumption in the article isn't a sufficient requirement for a solution to exist.

Author here - slightly overwhelmed by the response, but thanks for everyone's feedback! I never thought so many people would be as interested as I am in the lamp...