Kege Rend

Welcome to Kege Rend. I know the title of this page makes no sense but to decipher its meaning quite easy. I won’t give any hints given the cipher coding is quite simple.
I love mathematics especially playing with numbers. I did not quite love math when I was a kid since my mother would sit me down to mug up the multiplication table till 25. I started cheating. I found out tricks to calculate the result in the next sequence. For instance, I recall that I had remembered the table till 14 but I was yet to learn the table for 15 and I had already reached deadline. I did the following trick.
If 14 7s are 98 then 15 7s are 98+7 = 105. This is how I saved myself. It helped save me from a spanking but also ignited my interest in numbers.

When we divide by 9

1/9 = 0.111…
2/9 = 0.222…
3/9 = 1/3 = 0.333…
4/9 = 0.444…
5/9 = 0.555…
6/9 = 2/3 = 0.666…
7/9 = 0.777…
8/9 = 0.888…
9/9 = 1.000…
10/9 = 10*(1/9) = 1.111…
11/9 = 10/9 + 1/9 = 1.111… + 0.111… = 1.222…
NOTE:11/9 can also be perceived as 9/9 + 2/9 = 1.000… + 0.222… = 1.222…

This trick will come in handy a lot. It will help you save time. It gets trickier on two digit numbers and trickier furthermore as the number of digits increases. You have to find out the greatest number (divisible by 9) before the given number in numerator and do appropriate calculations.

For example, you are given 124/9
1. Finding the greatest number divisble by 9 and less than 124 which is 117.
2. 124 – 117 = 7 i.e. 124/9 = 117/9 + 7/9 = 13 + 0.777… = 13.777… rounding off upto two decimal digits we get 13.78
{Drakenkaul|13:59 07032017}

When we divide by 11

If you are interested in the process of this problem then please keep a rough notebook and a pen/pencil with you to get an idea of the unimaginable result. SO here goes the series:-

1/11 = 0.0909…
2/11 = 0.1818…
3/11 = 0.2727…
4/11 = 0.3636…
5/11 = 0.4545…
6/11 = 0.5454…
7/11 = 0.6363…
8/11 = 0.7272…
9/11 = 0.8181…
10/11 = 0.9090…
11/11 = 1.0000…
12/11 = 11/11 + 1/11 = 1.0 + 0.0909…

and so on!

This pattern is continuous unlike the one when we divide by 9. You might have observed that this pattern is following the multiplication table of nine after the decimal point and the pattern recurs after a complete division happens (11 divided by 11).

==Another way to learn the pattern ==
But there is another way to learn the pattern. All the digits follow the pattern of multiplication table of 9 (including the digits before decimal point). Let me elaborate- After a complete division step (when a number is divisible by 11) occurs, the product that we get in the future steps(till another complete division step occurs) is sum of the corresponding multiple of nine and the product of the previous complete-divison step. For example,

11/11 = 1.0 This is a complete-division step. Now, when we go further let’s say I want to find the product of 13/11. What I will do is this:-
The 13th multiple of 9 is 117. And the product of 11/11 (closest previous complete-division step) is 1. I will add them both and get 118. Now I will put a decimal point between the two 1s and get something like this : 1.1818.. And this is the answer for 13/11. Easy huh!

{Drakenkaul | 14:21 03072017}