I've always been fascinated with numbers. And I'm very lazy. Thus began my exploration of shortcuts to simplify maths. Since addition and subtraction were the simplest of all, I tried to search shortcuts to ease multiplication and division. This curiousity continued with every new concept that we learned in Maths. Percentages, percentages in terms of Profit and loss(or is it the other way round) and so on. My friends din't help either. Vivek and me used to calculate percentages for all the toppers. We'd always be stuck with some girls' score. As they were very secretive about marks (like some boys). But still managed to get most of it from reliable sources. And my first real Eureka moment happened after I learned the rule for divisibilty by 3 and 9. The rule: For a number to be divisible by 3 (or 9), the sum of the digits of the number should be 3(or 9) or its multiples. every number I came across was put to the test. I used to spend all my evenings with my Dad at the shop. And sitting there, I started applying the test to the numbers of the Vehicles that passed by. My challenge to self was to test as many numbers as possible. Just for the heck of it. The hunt for the shortcut begun. Soon , I observed that adding 9 was of no use. So I started leaving out the 9s. And then started forming 9s first and then counting the rest and so on. I was very excited to find out something new about numbers on my own. And told it to a few friends of mine. They asked " So what??". I could never answer that question. Not Yet.A few years later when all this seemed childish, I lost interest. More so when I heard my Dad's friend stating my "acute Observation" in a matter-of-fact manner, while discussing Numerology. (Probably, that's a reason why I hate numerology). It was common knowledge, it seems. And so it ended there.Last week I met a friend of mine after a long time. While in flashback mode, I told him about this. He said that CAT material has a lot of such shortcuts. So instead of searching the already -found and widely known techniques, better read it. He wasn't as discouraging as the last line seems to me. But that night, it all started again. This time it was (or were) multiples of 7. I found a pattern in the their sum of digits till you get them into single digits. And the next morning multiples of 13.
Here it is:
7---------7
14-------5
21-------3
28--10--1
35-------8
42-------6
49--13---4
56--11---2
63-------9
70-------7
77--14---5
84--12---3
and so on..the pattern was 7,5,3,1,8,6,4,2,9,7,5,3,1,8,6,4,2,9,7................
With 13, its a bit more complex though
13-------4
26-------8
39-------3
52-------7
65-------2
78-------6
91-------1
104------5
117------9
130------4
143------8
The pattern this time is with the alternate numbers 4 8 3 7 2 6 1 5 9 4 8 3 7 2 6 1 5 9.
What was still unknown to me, was the use of these patterns. I could not think of using it aywhere. Keeping that disappointment aside, when I told this to another friend of mine all he said was "Read CAT material, there's more useful stuff there." This was far better a response than the one that I feared. " So what????"
