Interesting concept. However, is it really a proof? If I removed piece #7 I'd have 24 boxes (12 white, 12 black) with which I could theoretically build a 6x4 rectangle, but I don't see how this would be actually possible with those pieces.
Maybe it only proves the negative, but not that there must be a solution.
Edit: there seems to be a solution for a 4x6 rectangle.
Maybe it only proves the negative, but not that there must be a solution.
Edit: there seems to be a solution for a 4x6 rectangle.