The Polish Hand Magic Trick "Revealed"

The Polish Hand Magic trick is an annoying little brain teaser that somehow works, although it looks like it shouldn't. Not only that, but the algebraic proof is totally unsatisfactory, in that it doesn't offer any insight into the mechanics of the trick. That frustration was brilliantly captured in this SMBC comic: http://www.smbc-comics.com/index.php?... The comic is based on one of the puzzles in The Puzzler's Elusion, a book by Dr. Dennis Shasha, «who apparently got it from "a smart and elegant Polish woman"». I'm quoting the cartoon, because I haven't read the book yet – but if you want to read it, it's available here: http://www.amazon.com/gp/product/1560.... You might also want to check out his other books, including this one from year 1709: http://www.amazon.com/gp/product/B011... (perhaps that's why they call him "Doctor"). The SMBC comic is rather old (June 2010), but I only found it a couple of weeks ago using their "Random" button. The comic's punchline is related to the very frustration I mentioned earlier. That gnawed at me in the background for a couple of days, until one night I decided to scratch that itch, and I started to investigate it further. This video is what I came up with; my wife and daughter are away from home, and this is how I ended up spending almost an entire day (in the video I'm saying half a day, but what with the post-processing, re-encoding and upload, I ended up spending way more time than I ever anticipated doing this thing). The "reveal" part is not perfect, I know – but it's better than anything I saw online (typically just the algebraic proof, or rants about how the trick is "useless", because it doesn't simplify multiplication – as if pulling rabbits out of hats was a legitimate rabbit growing technique). Amusingly, this apparently originates from Poland, and I'm Romanian – but I highly doubt anyone would ever describe me as "a smart and elegant Romanian man". One last thing: the thumbnail actually contains the gist of the "reveal" part; if you want to show off to your friends, you can just take a glimpse at the thumbnail and pretend you understood the whole thing at a glance. Happy bragging!