Blog Post #111 - Series #2 - Dissect and Analyze with the help of an all too familiar number!

In my earlier post, I had written about breaking down a complex problem into multiple smaller chunks using the example of finding n-th root of a number. In this post, we would look at the following - Given a particular scenario or use case or any problem statement, how important it is to evolve different perspectives and analyze various dimensions of the subject in focus. I would use a well known number in the digital world as an example just to illustrate how one could develop this skill by being patient and observant

65536 is synonymous with computers as 64 KB translates to 65536 Bytes. 65536 has also many factors of 2's multiple - 2 ^ 16, 4 ^ 8, 256 x 256, 16 ^ 4 and so on.

But a lesser known fact of 65536 is what I would focus on now given the theme of the current topic and it opens up a plethora of surprises. Let's dissect and break down 65536 digit by digit or carve out subsets, to reveal some amazing patterns

a) 65 - 13 x 5 (product of two primes)

b) 655 - 131 x 5 (product of two primes)

c) 6553 - Prime (product of two primes)

d) 553 - 7 x 79 (product of two primes)

e) 55 - 11 x 5 (product of two primes)

f) 53 - Prime

g) 653 - Prime

Go one step further and add or subtract combination of digits which are a subset

h) 65 + 536 = 601 - Prime

i) 655 + 36 = 691 - Prime

j) 655- 36 = 619 - Prime

k) 6 + 553 is 559 which in turn is product of two primes 13 x 43

l) 6553 + 6 is 6559 which in turn can be written as 7 x 937

m) 6553 - 6 = 6547 - Prime

n) 553 - 66 = 487 - Prime

Wow... A number which has 2 and its multiples as factors and is outright EVEN, exhibits a completely different behavior, when we dissect and analyze its digits or subset

This approach is pretty helpful in real life scenario, where given a use case or problem definition, it is imperative to break them down into multiple user stories or features and look at commonalities and patterns