 Enjoy, maybe even you can get 10 Cents to buy you a fancy inflatable pool!

## 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]

2. I was going to do what John did but a little voice said, “Nein, Nein, Nein”.  Do you think it was Herman Cain?

3. Robert A. McReynolds:
This is a cruel trick! I really want to go to Australia.

I was there, NBD, too many creepy crawlie things…

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