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One of the fascinating features of the 12 quints we explored early, back in 1977, is that they can form rectangles with anywhere from 3 to 12 pieces. A Progression, starting with 3 pieces as a 3x5 rectangle, then adding one piece at a time and forming incrementally larger rectangles, step by step, to 4x5, 5x5, 6x5, etc., is an especially elegant challenge. You could also start in reverse: make a 5x12 rectangle and remove one piece at a time, always re-forming a rectangle after each extraction.

Now comes Torsten Sillke, and he has calculated how many strings of such progressions exist. His computer found that the total number is 90554. Whoa. He also tells us that if the P is the last piece to be added, or the first piece to be removed, then there are only 119. It proves what we already knew: the P quint is always your best friend.

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