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

Blog Post #122: Tribute to the Maths Genius Srinivasa Ramanujan on his 133rd birth anniversary

As we near the end of an unprecedented year, here's a short blog post on the occasion of the birthday of an eminent personality whom I admire and revere the most - Mathematician Srinivasa Ramanujan

Dec 22nd 2020 marks the 133rd birth anniversary of the Mathematical genius and needless to say this day won't be complete without looking at some incredible number patterns

Let's look at few of them

a) 1887 + 2020 is 3907 which is a Prime number

b) 2020 - 1887 is 133 which is the product of two prime numbers - 19 and 7!

c) Add the digits of today's date in pairs - 22 + 12 + 20 + 20 and the resultant number is 74. Reverse of 74 is 47 and when you add both we get 121 which is a perfect square and a palindrome!

d) Now add the individual digits of the date - 2 + 2 + 1 + 2 + 2 + 0 + 2 + 0 which gives us 11 - square root of 121 in the previous step!

e)  Extract the 1st and last digits of both 1887 and 2020 - 17 and 20. Sum of these two numbers is 37 and difference is 3. Now multiply 17 with 37 and 3 - the resultant is 1887!!

f)  It does not stop there.. Hold on! 

133rd birth anniversary is special as well in many sense

- 133 is a product of two primary numbers as we saw earlier

- 133 is also a sum of two cubes - 125 and 8 (5 ^ 3 + 2 ^ 3)

- 133 is difference of two perfect squares - 169 and 36 (13 ^ 2 - 6 ^ 2)

I am sure we can go on and on as there are infinite possibilities when we start talking about the Mathematical genius and humble tribute to "The Man who knew Infinity"!

Blog Post #121 - 12/12/2020

 Time flies and we are already in December in an year which has been unprecedented in nature and we continue to look for positives before we step into 2021

12/12/2020 is a bit unique many ways and today's blog post is around some of the patterns that we see around this date which also coincides with the Computer Science Education Week (Dec 7th to 13th)

1. 12 + 12 + 20 + 20 is a perfect square (64) which is a core number in computer/digital world and it is a sheer coincidence with Computer Science Education Week 

2.   12 * 12 gives 144 and 20 * 20 is 400. Difference of the two is again a perfect square (256) and square of 256 is 65536 which again is a most familiar number in Computer world

3. The best is always reserved for the last

Sum of the digits - 1+2+1+2+2+0+2+0 = 10

Sum of the squares of the digits - 1 + 4 + 1 + 4 + 4 + 0 + 4 + 0 = 18

Sum of the cubes of the digits - 1 + 8 + 1 + 8 + 8 + 0 + 8 + 0 = 34

Sum of the fourth power of the digits - 1 + 16 + 1 + 16 + 16 + 0 + 16 + 0 = 66

Notice the sequence - 10, 18, 34, 66

The difference between successive numbers is 2 ^ 3, 2 ^ 4, 2 ^ 5 and you could guess what would be the next number in the series without doing any further complex maths!

Maths is fun and 12/12/2020 is just another reason why we can feel more optimistic as we move towards 2021