School-Safe Puzzle Games

## Artemis’s Study

Makada let me know about this neat little number magic trick; can any of you figure out the math behind it? By the way,  so far only Hex and Aaronlau have been able to figure out the Farmer math puzzle! (update, couple more added to list, check post)

### 4 Comments to “Artemis’s Study”

1. Migrated | Profile

Well, it didn’t say you couldn’t repeat the digits when choosing the first number so I chose 11 as my number. Rearranging the digits would get me 11. Subtracting them would get me 0. Then it just stays as zero for the rest of the thing because I can’t circle zero. After punching zero into the computer, it said I circled ‘9’ which cannot be true.

So…I don’t know how that helps with figuring out the maths behind the algorithms.

2. poopsicle | Profile

after the subtraction step, you will always be left with a multiple of 9

the sum of the digits of any multiple of 9 is always a multiple of 9

the multiplication step doesn’t matter, since you will still have a multiple of 9

if the sum of the digits you enter is x, the answer is just 9-(x mod 9)

3. poopsicle | Profile

and here is a simple explanation of why you will always have a multiple of 9 after the subtraction:

= (A*1000+B*100+C*10+D)-(C*1000+A*100+D*10+B)
= A(1000-100)+B(100-1)+C(10-1000)+D(1-10)
= 900A + 99B – 990C – 9D
= 9(100A + 11B – 110C -D)

ABCD -> CADB is just an example, this will work for any rearrangement

4. syker | Profile

use your thumb and forefinger as the 2 digits