Blog #134: Welcoming 2022 with more hope and optimism!

2022 is here and along with it more hope and optimism as we navigate our way out of the pandemic that changed the world order and gave us a new perspective of how to approach life in general

A short mathematical note to welcome 2022 with Hope and Optimism as the "Prime" and "Unique" reason as we look forward to getting back to normalcy and have more in-person interactions with friends and family members without getting anxious about what's around!

a) 2022 + 2021 (the year before) gives 4043 which is a product of two "primes" - 13 and 311

b) 2022 + 2023 (the year after) results in 4045 which is again a product of two "primes" - 5 and 809

c) Now let's look at the factors of 2022 - It can be written as 337 x 6. When you look closely at 337, it is a "prime" number and more interestingly, the anagrams of 337 which are 373 and 733 are also "prime"!

d) 2022 is very interestingly placed between two square pairs. Take a look

The two even squares greater than 2022 are 2116 (46x46) and 2304 (48x48). Now difference between 2116 and 2022 is 94 while between 2304 and 2022 it is 282. 282 is 3 times 94 and also if you add the square roots (46 and 48), we get 94 again!

Now let's take a look at the even squares lesser than 2022 - 1936 (44x44) and 1764 (42x42). We would observe a similar pattern as above. The difference between 2022 and 1936 is 86 and between 2022 and 1764 is 258. 258 is 3 times 86 and if you add the square roots (42 and 44), we get 86 again!

e) Add 20 and 22 and we get 42. Reverse of 42 is 24 and when we multiply both we get the number 1008 which has a unique place in the field of astrology, spirituality, astronomy among many other fields

As we could see, 2022 has its own prime and unique properties and that personally gives me more hope as we look forward to this New Year

Wishing everyone a very Happy, Prosperous and Healthy 2022

#Hope #Optimism #2022

Blog #133: 2021 Recap - Teamwork and Collaboration at its best

If I look back at 2021, it was filled with full of challenges as well as opportunities for many of us both on the personal and professional front. On the professional side, what stood out to me within Mr. Cooper Group was the seamless collaboration, teamwork and commitment exhibited across teams spread across multiple locations, where employees came together, partnered with each other and delivered towards a common cause. 

I constantly saw people from Technology and Business functions working on new automation initiatives and ideas as well as employees from Business enabler functions like HR, Facilities, Finance partnering with their Business teams and innovate at every possible opportunity - Extremely proud of this work culture and credit goes to each one of the Coopers and Xomies

In the mathematics world, Numbers show a striking similarity and behavior - Whether it is an odd or even or prime number or a perfect square or cube, they display amazing patterns when they combine together and create magic under different circumstances

Here are few of my favorites and this is dedicated to all my team members across India and US.

1) 17 and 29 are two prime numbers on the face of it and so unique in that aspect. 

    a) Both are odd numbers but also when you look deeper, 17 and 29 are sum of two perfect squares - 17 is 16 + 1 while 29 is 25 + 4!

   b) Now when they combine together they become more special..1729 is Ramanujan number which doesn't require any introduction!

   c) Add the individual digits 1+7+2+9 = 19. Reverse of 19 is 91 and when you multiply both we get 1729 again!

2) Next in line 16 and 81. Both are perfect squares to begin of two other perfect squares but one of them is even and other is odd. That's how unique they are to begin with

Now let's see what happens when they combine together in various forms and shape!

     a) 1681 - Yet another perfect square (41 ^ 41)

16 x 81 - 1296 which is a perfect square again but it doesn't stop there. Anagrams of 1296 are 9216 (perfect square), 2916 (perfect square again!)

     b) Now add all the digits of 16 and 81, one by one..1 + 6 + 8 + 1 = 16! One of the original number and also a perfect square

     c) Add the digits in pairs - 16 + 81 = 97 which is the largest 2 digit prime

     d) Finally 168 + 1 is 169 whose square root is 13 and if you add the square roots of 16 and 81 you get 13 again!

3) Borrowing from one of my earlier blog posts, I have randomly selected two prime numbers 29 and 59 for this exercise

     a) Next form a 4 digit number combining 29 and 59 which gives us 2959. 2959 is not a prime but again a product of two primes! - 11 and 269

     b) Let's go a step further and form a 5 digit number with 11 and 269 which gives us 11269. What's interesting is that 11269 follows the same pattern - It is not a prime but again it is a product of two primes - 59 and 191 (As a side trivia, check how 59 appears across multiple numbers here)

    c) Next in line - the 5 digit number 59191 (59 and 191 together). Voila - 59191 is also a product of two primes 11 and 5381!!

   Tempted to go one step further?

    d) 115381 - this is a product of 7 and 16483 while 16483 in turn is a product of 53 and 311

        Though in some sense the sequence is "broken" as 115381 is a product of three prime numbers instead of two but we could see how these numbers come together and deliver something unique

If we look at the above 3 examples, we notice that numbers with unique attributes and background, when combined together through various Mathematical operators, deliver something very unique. Drawing a parallel, it is up to each one of us to identify and nurture the talent in every individual within the team and enable them with all the support required to collaborate under different circumstances to deliver towards a common goal. Believe me, each of those teams would innovate as they move along and create an ecosystem which is best in class

Thanks again to all my team members, colleagues and business partners for a wonderful 2021 and look forward to 2022

#WeAreMrCooper #WeAreXome #NumbersAreFun #Teamwork #Collaboration #ThankYou

Blog #132 - Srinivasa Ramanujan Birthday special

As we take a step closer to the beginning of a New Year, here's a short blog post on the occasion of the birth anniversary of the great mathematician Srinivasa Ramanujan - The Man Who Knew Infinity

Dec 22nd 2021 marks the 134th birth anniversary of the Mathematical genius and here's a humble tribute from yours truly to undoubtedly the greatest Mathematician of the last century

Let's look at few unique number patterns

a) 1887 + 2021 is 3908 which is a sum of two perfect squares 3844 and 64

b) 1887 can be represented as 1936 - 49 (44 ^ 2 - 7 ^ 2) while 2021 can be expressed as 2025 - 4 (45 ^ 2 - 2 ^ 2). Difference of two perfect squares

c) Now for the Ramanujan number itself to do some magic - 1729

1887 - 1729 = 158

Add 2021 and 158 and we get 2179

Now check this out

2021 - 1729 = 292

Add 1887 and 292 and bingo we get 2179 again!!

And do note that 2179 is the anagram of 1729!

Ramanujan Number at its best

d) In the previous step let's do subtraction instead of addition and see what happens

2021 - 158 = 1863 which is 1729 + 134 (Ramanujan number + 134th anniversary)!

1887 - 292 = 1595 which is 1729 - 134

(Ramanujan number - 134th anniversary)!

I am sure we could find more such interesting patterns especially when it is related to the Mathematical genius

#MathematicalGenius #srinivasaramanujan #TheManWhoKnewInfinity

#BirthAnniversary #NationalMathematicsDay

Blog #131: Independence Day Special!

As India enters her 75th year of independence, this blog post is a small dedication from my side to our nation

a) 15 + 08 + 20 + 21 is a perfect square 64 which is unique in many ways - 64 is 8 ^ 2, 4 ^ 3, 2 ^ 6 and the smallest number with exactly 7 divisors

b) 1508 + 2021 happens to be a prime number 3529. May be wondering what's so unique about that - Check this out. Add 1947 to 3529 and we get 5476 which is a perfect square of 74! We have completed 74 years of Independence and entering 75th!

c) Let's look at 15 and 08 - Half of 8 is 4. Add that to 15 and we get 19. No subtract 08 from 15 and we get 7. Prefix the other 4 left out from the earlier step and you get 47 - concatenate 19 and 47 to get 1947!

d) The next pattern is incredible - Let's look at the sum of the squares in pairs

15 ^ 2 + 8 ^ 2 = 289 = 17 ^ 2 (Pythagoras)

20 ^ 2 + 21 ^ 2 = 841 = 29 ^ 2 (Pythagoras again!)

17 and 29 when combined together gives the ever famous Ramanujan number

15-08-2021 is truly awesome and one of a kind! Very rarely 2 pairs of squares within the same number demonstrates such a pattern

#IncredibleIndia 

Blog #130: Dedicated to Subedar Neeraj Chopra!

Tokyo Olympics 2020 just came to an end and a fairly successful one considering so many uncertainities surrounding the Games due to COVID

Indian team had some great moments right from Day one when we won a Silver medal thanks to the heroics of Mirabai Chanu and also had some heartbreaks in between but the best was reserved for the last day when Subedar Neeraj Chopra won the Gold in the Javelin event and made this a memorable event for a billion plus people including yours truly

Here's a small Mathematical tribute for the Golden Boy of Javelin revolving around the magic number 8758 (87.58 metres was the winning throw!). 8758 has some special qualities compared to its peers and here are a few

a) 87 and 58 are successive multiples of 29 (multiples of 3 and 2)

b) His birth year is 1997 - 19 + 97 is 116 which is again a multiple of 29 (4 times)!

c) One of the anagrams of 8758 turns out to be 8758 again!

d) 87 + 5 + 8 is a perfect 100 and I am sure that would be his next target in 2024 Olympics!

e) Multiply all the digits and we get 2240. Anagram of 2240 is 2024 and we wish another Gold from Neeraj in Paris!

f) Add all the digits of 8758 till you reach a one digit number - 8 + 7 + 5 + 8 is 28, 2+ 8 = 10. 1+ 0 = 1. Needless to say he is the Numero Uno now!

Coincidentally I happen to share the birthday with the Subedar and feel chuffed about it!

Blog #129: The Catalyst

The Catalyst that is needed to provide multiplier effect without losing focus of the final destination or goal - Explained through some interesting number pattern

Whether it is in professional or personal life, there is always that tiny little spark or catalyst that pushes us out of slumber and helps overcome the inertia or come out of status quo. 

This catalyst pushes an individual out of the comfort zone providing a new perspective outside the "bubble" he/she was in and at the same time helps move towards a common goal resulting in a much larger outcome (the 5x or 10x multiplier as they call it) 

Let's see some unique number patterns where the introduction of a single digit (The Catalyst) results in an outcome with multiplier effect but all of them navigate towards a similar goal

Look at 11x11 to start with - We get 121. Now insert 5 (The Catalyst) as the second digit from the left and the resulting number is much larger square 1521 (39 x 39). Add 11 and 39 and we get the result as 50 (Our final goal)

On similar lines

12x12 = 144. Insert 4 (The Catalyst) as the second digit from the left (or even towards the end in this case) and the resulting number is a 4 digit square again 1444 (38 x 38). Add 12 and 38 and the result is still 50 (Our final goal)

13x13 = 169, Insert 3 as the second digit from the left and result is 1369 (37x37). 13 + 37 = 50

14x14 = 196, Insert 2 as the second digit from the left and result is 1296 (36x36). 14+36 = 50

15x15 = 225. Insert 1 as the first digit towards the left and result is 1225 (35x35). 15 + 35 = 50

This series is unique in its own sense where the addition of one digit as The Catalyst resulted in a much larger outcome but the overarching goal was still in focus throughout

We can find similar patterns for numbers 23, 24, 25 with the final target as 100

23x23 = 529, Add 9 as the second digit and we get 5929 (77x77). 23+77 = 100

24x24 = 576, Add 7 as the second digit and we get 5776 (76x76). 24+76 = 100

25x25 = 625, Add 5 as the first digit towards the left and we get 5625 (75x75). 25 + 75 = 100

If we need to come out of our comfort zone or break the status quo, all we need is "The Catalyst" to act as the trigger and product results at higher productivity levels (multiplier) but without losing focus on our final destination or goal

Let's find our own Catalyst!

Blog Post @128: Rally around the Individual contributor - 333031!

Individual Contributor is a loosely used word in the corporate world and normally refers to people who have a unique skillset whether it is Technology or domain or process related and for some strange reason, are assumed to be working on their own without the need of having a team

While technically this person may not have anyone reporting to him/her, this role is a critical cog in the wheel for any organization and has to closely collaborate with everyone else in the team to achieve the final goal set for the group. The individual becomes a key performer and a star contributor only after he/she understands the broader team needs and also the rest of the team members rally around this person once they realize the value he/she brings to the table

This blog is dedicated to the technical architects, consultants, domain experts and many other individual contributors, whose potential is best leveraged when the ecosystem understands their expertise better and the individual also mentors/grooms every team members they get to work with

I need not go too far to find such a number and have chosen the Zip code of my Alma Mater, BITS Pilani, Rajasthan India - It is the magical 333031! I have written about this number in the past and thought this is the right opportunity to explore deeper

1. To start with, 333031 is somewhat unique like an individual contributor and it is a Prime Number

2. Now it doesn't stop there - 33331, 3331, 331, 31 which are subsets of 333031 are all prime! Such is the diversity this number brings in just like an individual contributor role is expected to have a breadth of skillsets!

3. Let's look at the number 65536 - very well know in the computer world and is a product of multiple factors. It could be written as multiples of 2, 4, 16, 64 and truly a number which is a conglomeration of multiple smaller factors or team members. 

65536 x 5 is 327680 which is equivalent of a larger team, 5 times the original size working together on a transformational initiative. Now add a prime number 5351 to 327680 and you get the answer as 333031 which is our Star individual contributor to start with! This is a classic example of how someone with unique skillsets can be part of a larger team comprising of smart individuals and constantly enable them to deliver towards a common goal!

4. On similar lines, like we saw in one of the earlier blog post, 2520 is the lowest 4 digit number which has factors from 1 to 10. In essence, 2520 is a combination of diverse set of numbers (team members with varying skillsets) coming together

Let's look at the last 3 digits of 333031 in reverse order (130). Multiply 2520 and 130 and we get 327600. When we add another prime number 5431 to 327600 we get back 333031! Yet another example of how individual contributors (prime number equivalent) have to work hand in hand with the larger team to successfully deliver the tasks

5. 333031 itself brings lot of unique attributes to the table just like a Tech Arch or Tech Lead or Domain consultant or Network Engineer is expected to bring unique skillsets

5a. Product of its non-zero digits is 81 which is a perfect square. 

5b Sum of all of its digits is 13 which is a prime number on its own

5c Sum of the squares of all of its gitis is 37 which is a prime number again and when multiplied with 9 it gives 333 which is the first 3 digit of the number!

5d Sum of the cubes of all of its digits is 109 which is again prime and 109 in turn is sum of two perfect squares - 100 and 9!

Truly 333031 turns out to be a very unique number, having multiple key attributes that are required in an ecosystem and at the same time delivers the best when it is in the company of a larger team (numbers like 65536, 2520 in this case as we saw above)