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) 

Blog Post #127: Leveraging the best of contrasting personalities to create a winning team!

In the corporate world, time and again we come across two individuals in a project team or leadership roles who are extremely good at what they do, very smart but have very different personalities - one could be soft spoken but still pretty assertive in terms of the decisions he/she takes while the other may come out as a critic but is highly regarded for his/her inputs. Both of them bring in lot of value to the team and have to be groomed/managed to ensure that they deliver towards a common goal

Given this context, I was inspired to look at the numbers 1729 and 2520 which are very unique in their own sense and stands out from the rest but when they operate together, the outcome is a series of amazing patterns that we may not have expected in the first place. Listing down a few of them

To begin with 1729 and 2520 are unique in their own respect for the following reasons

1729 is the famous Ramanujan Number and the lowest 4 digit number which can be expressed as sum of two different cubes - 10 ^ 3 + 9 ^ 3 = 12 ^ 3 + 1 ^ 3

2520 is the lowest 4 digit number that has factors from 1 to 10

Let's bring them together and rock and roll!

1. Stating the obvious - 1729 is odd and 2520 is even but that's how different they are!

2. 1729 + 2520 gives 4249 and when you closely observe 42 and 49 are successive multiples of 7

3. Carrying on from the above with 4249 as the sum of these two, let's add 42 + 49 and the resultant is 91. Now 91 multiplied by its reverse 19 gives back 1729! That's the synergy we are looking for

4. Go one step further - 17 + 29 gives 46 while 25 + 20 yields 45. If you add 46 + 45, we again get 91 which is a factor of 1729 as mentioned in the previous step

5. Now add all the digits of 1729 and 2520 one by one and we get 28 which is a factor of 2520 in turn! 

6. Both 1729 and 2520 are multiples of 7 - 247 x 7 and 360 x 7. Now both 247 and 360 can be written as difference of two squares - 247 is 256 - 9 while 360 is 361 - 1. Beautiful isn't it! 

7. Multiply all the non-zero digits of 1729, 2520 one by one - 1 x 7 x 2 x 9 x 2 x 5 x 2 and the resultant number is 2520 - BINGO! That's awesome and a classic example of how these two bring the best when they "work" together

As we could clearly see, 1729 and 2520 are unique in their own respect but when they collaborate together and we leverage their unique properties (offering), the results could be amazing. 

This is very true in a corporate world as well and all it requires to identify the strengths and potential of the individuals to create a winning team

Blog Post #126: Dedicated to someone truly special and who is bringing in a change

 I decided to dedicate this post to my friend and ex-colleague, Sujith who just recently completed his 2 decade work anniversary at Infosys. Coincidentally we both started few months apart back in 2001 at Infosys and right from the time I got to know Sujith, he came across someone who was lively, always itching to do something new and more importantly wanted to make a difference!

The number 13649 is synonymous with Sujith's tenure at Infosys which started back in 2001 and just like him, this number has so many special and perfect qualities and why should we be surprised!

Here we go

a) To start off, 13649 is a "Prime" number and has a unique place in the number history! If you add all the digits of this number 1+3+6+4+9 we get 23 which is again a prime!

Let's go deeper into the number itself  - 13649 is not only prime but "perfect" in many sense

b) Look at first, third and fifth digits and you get 169 which is a perfect square and turns out 169 square root is 13 which is the first two digits of the number!

c) 1, 36, 49 are perfect squares again!

d)  Digits two, three and four is 364 and you look closer there are two perfect squares again - 36 and 64 and what more.. If you add both you get 100 which is a 10 ^ 2!

Last but not the least the number 13649 is itself formed by 5 different digits, each one of them is unique in their own respect and that's how Sujith has brought together people from all walks of life to make a difference through Maatram! 

Blog Post #125: Unique attributes of the number 125 - The nonchalant allrounder!

This is my 125th blog post and decided to pen down about the number 125 itself as it has some very unique attributes apart from some of the very obvious ones

Drawing a parallel to the corporate world, 125 is like the all-rounder in any project team - multi-skilled, possess unique attributes compared to its peers and more importantly don different avatars or wear various hats when confronted with different external situations and unknowns

1. For starters, 125 is 5 ^ 3 and let's table it as the base attribute to begin with

2. 125 can be written as the sum of multiple squares (combination of various skillsets) and few are listed below

     a) 100 + 25 = 125

     b) 121 + 4  = 125

3. 125 has a very rare attribute which not many numbers can boast of

     125 is 5 ^ 3, Sum of the digits 1 + 2 + 5 is 2 ^ 3 and 512 which is an anagram of is 8 ^ 3 (can be also written as (1 + 2 + 5) ^ 3

4. Further more look at the following pattern sequence where you prefix 1 to 9 to 125 - drawing a parallel to how an individual would react to varying situations while handling a project milestone

    a) 1125 = 35 ^ 2 - 10 ^ 2

    b) 2125 = 45 ^ 2 + 10 ^ 2

    c) 3125 = 55 ^ 2

    d) 4125 = 65 ^ 2 - 10 ^ 2

    e) 5125 = 75 ^ 2 - 20 ^ 2 - 10 ^ 2

    f) 6125 =  75 ^ 2 + 20 ^ 2 + 10 ^ 2

    g) 7125 =  85 ^ 2 - 10 ^ 2

    h) 8125 =  85 ^ 2 + 30 ^ 2

    i) 9125  =  95 ^ 2 + 10 ^ 2

  5. And finally the blockbuster - 125 squared = 15625. Let's go deeper one layer after another 

      a) 15625 = 125 ^ 125

      b) Peel off 1 and you get 5625 which is 75 ^ 2

      c) Peel of 5 and resultant is 625 which is 25 ^ 2

      d) Peel of 6 and resultant is 25 which is 5 ^ 2

It is not just the breadth of skills that someone exhibits but also the depth of understanding, which is important as we peel/remove one layer after another in the scenario above, that makes someone a true all-rounder and Man Friday that any project team would love to have!

#MatheMagic #AnandMathsBlog 

 

Blog Post #124: Revisiting good old Armstrong numbers

Few days back, I was interacting with about 10-15 students last week of a Government school over video call and one of the topic was around 3 digit Armstrong numbers and what makes them special. It made a fascinating discussion with the kids as they started looking for out-of-the-box answers

That inspired me to revisit these numbers and look at some interesting patterns that emerge

Let's look at all the 3 digit Armstrong numbers to begin with - 153, 370, 371, 407

For starters, these are called so, as the sum of their digits raised to the power 3 equals to the number itself

1^3 + 5^3 + 3^3 for e.g is 153. 

For this post let's consider 153 and its anagrams and we would be amazed by the unique characteristics they demonstrate

a) 153 also happens to be sum of two squares (12 ^ 2 + 3 ^ 2) and difference of two squares (13 ^2 - 4 ^ 2)

b) 135 which is an anagram of 153 is a difference of 12 ^ 2 - 3 ^ 2

c) 351 which is also an anagram of 153 is a sum of two cubes - 7 ^ 3 + 2 ^ 3

d) 513, another anagram of 153 is sum of two cubes - 8 ^ 3 + 1 ^ 3 and difference of two squares - 23 ^ 2 - 4 ^ 2

e) 315 is difference of two squares again 18 ^ 2 - 3 ^ 2!

f) Now let's add two perfect squares to 153 and see what happens with the resulting numbers

153 + 81 = 234 and 153-144 = 09 and when we concatenate 234 and 09 we get 23409 which in turn is 153 * 153! (153 squared)

In summary, 153 is a truly multi-faceted number and can don various hats with ease, adapting to external conditions

Blog Post #123: Welcoming 2021!

As 2020 drew to a close, it is time to welcome a brand new year with all hope and optimism and here's a small Mathematical note from my end

Some of these were already published in social media in recent days and so not necessarily unique for this post but it is amazing to see how many such patterns you could find when you look at 2021

a) 2021 is a difference of two perfect squares - 2025 and 4 (45 ^ 2 and 2 ^ 2) and hence applying a ^ 2 - b ^ 2 formulae, it ends up as a product of 2 prime numbers as well (47 and 43)

b) Prefix 1 to 2021 and you get a perfect palindrome 12021 which is a product of two prime numbers 4007 and 3!.

c) Suffix 1 to 2021 and you get 20211 which again a product of two prime numbers 3 and 6737

d) 20 + 21 is 41 which is again a prime and the subsequent two prime numbers when multiplied gives 2021! (43 and 47)

e) Sum up the digits of 2021 - 2 + 0 + 2 + 1 = 5 and it is a prime again!

f) 43 and 47 are the prime factors as we saw earlier. Now prefix 1 to both 43 and 47 and multiple the two - 143 * 147. The resultant number is 21021 which has a close resemblance to 2021 (1 inserted as the second digit)

g) Now add 2020, the year gone by with 2021 and you get 4041 which is again a product of two primes - 3 and 1347

These are other "prime" reasons why we should hope for the best in 2021 :)

Happy New Year again