8 thoughts on “Your next vacation destination!”

  1. [spoiler title="How it works"]
    This works due to the mathematical mechanism of “Casting out nines”.  Here are the expressions evaluated by each of the steps in the process.

    1. x (selected digit)
    2. x × 3
    3. (x × 3) + 3
    4. ((x × 3) + 3) × 3 = (3 × (x × 3)) + (3 × 3) = (x × 9) + 9

    Now since the base of the number system is 10, the process of summing the digits of a number will discard nine multiplied by any number, leaving only the remainder.  Hence, the first term, (x × 9), contributes nothing to the result, which is always 9.

    In step 1 you can actually choose any number from 0 to 9.  Casting out nines works because the sum of the digits of 9 times any number is always zero modulo 9.
    [/spoiler]

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  2. The whole thing works by adding nine. Adding nine means to carry a one to the ten column while decreasing the number in the one column.
    09=(10-1)

    18=(0 + 1)10 + (9-1)

    27=(1 + 1)10 + (8-1)

    36=(2 + 1)10 + (7-1)

    Since we have a base 10 system. One can divide by two or multiply by 5 and shift the decimal to get the same result. This means also multiplying by 2 means the same as dividing by 5 and shifting the decimal.
    Say you want to figure out what 625 x 5 is. That seems daunting but dividing by 2 is not. Therefore 625/2 is 312.5. Move the decimal point to the right and you get 3125 which is 625 x 5. Now 3125/5 can be done by shifting the decimal on 3125 to the left and getting 312.5. Then multiply by 2 to get the answer 625. This is because 0.5 equals 1/2 and 2 equals 1/0.5.

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  3. [video width="480" height="206" mp4="https://www.ratburger.org/wp-content/uploads/2020/08/b96051c4ab5d4253be074a7887a97dc9.mp4" loop=yes][/video]

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