4 Replies to “Crystal Ball”

  1. Ah, because every time you reload the page the symbols change. ilusion + math is a cool combination. sorry to ruin the fun. 🙂

  2. ah… yes… and the second time i got the symbol to show by just picking a random number, i did pick the symbol next to the number 81, 9×9, of course! gosh it’s good to know smart people! thanks!

  3. Casting out nines. Anytime you add digits and subtract them from the original number you get a multiple of nine, and as you’ll notice all the multiples of nine have the same symbol.

    Say the original number is 71–that is
    (7×10) + (1×1) from which you subtract (7×1) + (1×1) the sum of those digits.

    7×10 – 7×1 is the same thing as 7x(10-1) (remember that distributive rule or factoring?) which is 7×9
    1×1 – 1×1 = 0 so all you have is the 7×9

    so say T is your tens digit and N is your ones digit. The number TN is the same as Tx10 + N x 1

    so using that instead of 7 and 1 you get
    Tx10 + Nx1 – (T + N which is the sum of the digits) =
    Tx10 + N – T – N so the N’s cancel each other out and you get
    T x 10 – T which is 9 x T which has to be a multiple of nine!

    So you’re mind reading magic is one of the coolest properties of math!

  4. yes, okay… i just barely follow that… so that whichever numbers i pick, it’s going to be a multiple of nine… and all multiples of nine have the same symbol.

    but… i did it once and got the right symbol. a snow flake. then i did it again, this time just plain visualizing, very clearly and clicking. and got the right symbol again. different symbol.

    i clicked again casually without visualizing anything and got a third symbol.

    what happened? if all nines are same symbol, why does it generate different symbols each time?

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