Blog #151: All about 9/25/2025

There has been multiple posts/videos around the specialty of today's date - 9/25/2025 since the next similar sequence won't happen till 2116! 9 is 3 ^ 2, 25 is 5 ^ 2, 2025 is 45 ^ 2. 46 ^ 2 is 2116 and that's going to be close to 90+ years from now

 

While this is certainly unique, the date 9/25/2025 also exhibits other amazing patterns and that prompted me to write a short blog post pretty quickly after the OTP/Palindrome one i had shared few days ago

 

Let's see some of the patterns at play for 9/25/2025 - looks pretty simple but not so apparent. That's the beauty of Maths and Number patterns

 

1. 9 ^ 2 * 25 gives 2025 (Month ^ 2 * Day = Year)

 

2. Add the digits - 9 + 2 + 5 + 2 + 0 + 2 + 5 = 25 which is the Day as well as a perfect square

 

3. Let's alternate addition and subtraction - 9 + 2 - 5 + 2 - 0 + 2 - 5 and the resultant is 5 which is the square root of the Day!

 

4. Now multiple all non-zero digits and the resultant is 1800. 1800 + (9 * 25) = 2025 again! 1800 + (MM * DD) = YYYY

 

5. Next add the non zero digits in pairs - 92, 52, 25 and the resultant is 169 which is a perfect square again (13 ^ 2) and its reverse that is 961 is also a perfect square (31 * 2) - Note that 13 and 31 are also reverse of each other

 

6. The numbers 9 and 25 are part of the Pythagoras pair - 9 + 16 = 25 and there were even various social media posts last week around it when the date was 9/16/25. 2025 is not left far behind and it is also part of a Pythagoras pair - 729 + 1296 = 27 ^ 2 + 36 ^ 2!

 

So while 2116 is the next perfect square as far as Year is concerned and it is 91 years away, let's be at awe on what 9/25/2025 has to offer and live in the current moment :)

Blog Post #150: OTP and Palindrome!

Received an OTP as part of one of my regular online transactions and when i saw the number 347743, i told my wife that it is a palindrome. Ofcourse she gave me a surprised look and moved on with rest of the chores that she was focusing on!! 

Given my penchant towards numbers, I started analyzing this in more detail and it was pretty refreshing to unearth some of the obvious and not so obvious properties. 

347 and 743 are the two numbers in consideration and to draw a parallel to the corporate world, this is a great example of how complementary skillsets within the team can help galvanize everyone to come together to achieve a common goal

Let's start looking at some of the characteristics exhibited by the number

1. Both 347 and 743 are prime numbers to begin but 347743 has 11 as one of the factors given it was formed by 347 and its reverse!

2. Subtract 14 from 743 and it gives a perfect square (729). Now give whatever has been subtracted from 14 to 347 and the sum is again a perfect square! (361). Talk about balancing act!

3. 347, 349, 353, 359, 367 are successive primes and the difference between successive primes is 2, 4, 6, 8 (this is quoted in multiple mathematics articles). Now look at the reverse of these numbers - 743 is a prime as we already know, 943 is a product of two primes (23 and 41), 353 is a prime, 953 is a prime and 763 is again a product of two primes (7 and 109)!

4. From the original number 347743, let's do the following. Though some of these are pretty obvious in hindsight, it looks interesting on how it unfurls when we analyze deeper

a) Remove both 7s first and we get 3443 which is a multiple of 11 and 313 ( a palindrome). 

b) Remove both 4s and we get resultant number as 3773 which is a multiple of 343 and 11. 343 is a palindrome as expected but it is also 7 ^ 3 and unique in its own ways (3 + 4) ^ 3 is 343!!

c) Remove both 3s and we get resultant as 4774 or since we are dealing with odd numbers let's go with 7447. 7447 is again a product of two primes - 11 and 677

5. Now let's add 347 and 743 and the outcome is 1090. To begin with, 1090 looks pretty much like any other even number but here is the fun part 

a) It can be also written as Sum of two squares - 33 ^ 2 + 1 ^ 2.

b) What's more amazing is that it can be written as 32 ^ 2 + 66 and 34 ^ 2 - 66. 1090 exhibits such unique properties spread across 3 successive squares

6. Last but not the least when we multiply 347 and 743 the resultant is 257821. At first glance, there isn't much to look into except it is a 6 digit number and product of two primes. Dig a bit deeper - Take 821 and reverse it to get 128. 128 *2 + 1 is 257!

Numbers are fun as always and for me the trigger for this weekend post was a harmless OTP which turned out to be a very interesting palindrome showing lot of synergies just like we would all expect within a team in our corporate world!

Blog #149: The curious case of 15625!

Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!

Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!

Decided to pen a quick blog thanks to the message from my friend and ex-colleague Prasanna Aravamudhan over the week-end. He forwarded me a note that today's date in DDMMYY (if you ignore the zero!) format is a perfect square. 15/6/25.. 15625 and that acted as a trigger for me to write about 15625 - a true versatile allrounder that each one of us would like to have in our team!

Hide quoted text

Here are some interesting stats about the number

1. As we know by now, 15625 is a perfect square of 125

2. Remove the leading number 1 and the resultant is 5625 which is also a perfect square of 75! 

3. Remove the first 2 digits (15) and the resultant is 625 which is also a perfect square of 25!!

4. Remove the first 3 digits (156) and the resultant is 25 which turns out to be a perfect square of 5!!!

5. 15625 also turns out to be a perfect cube of 25!

Now for some deeper insights on this perfect square

6. The reverse of 15625 (52651) turns out to be a product of two prime numbers - 37 and 1423. Unlike 15625 which has 5 and other factors, 52651 is a odd number with only two prime factors

7. Add 156 and 25 and the outcome is 181 while if we subtract 156 and 25, the resulting number is 131. Both 181 and 131 and palindrome primes!

8. 15625 is sum of multiple perfect squares - 100 ^ 2 + 75 ^ 2, 120 ^ 2 + 35 ^ 2

9. Sum of all the digits of 15625 is 19 which is a prime number

10. Sum of the squares of all the digits of 15625 (1+25+36+4+25) is 91 which is a product of two primes also reverse of 19 in the previous step!!

Blog #148: Something about 153 and Year 2025!

My earlier post a week ago, was around welcoming 2025 and when I started thinking about what should be the next blog about, I did not have to spend lot of time - Enter the ever versatile and amazing Armstrong number 153!

153 is the first and smallest Armstrong number and it is special in many ways and I was sure that somewhere there is a link between 153 and the perfect square year of this millenium - 2025

Let's see how special 153 is before establishing the link with 2025

a) For starters 153 is an Armstrong number and hence sum of the cubes of its digits equal the number itself

b) 153 is the sum of two squares 12 ^ 2 and 3 ^ 2 as well as difference of two squares 13 ^ 2 and 4 ^ 2!

c) 153 can be written as (9 ^ 2) + 72 as well as (15 ^ 2) - 72 - WOW!

Now let's look at what happens when 153 is flipped over - we get 351 which is not an Armstrong number but watch these similarities between 153 and 351

d) 351 can be written as  18 ^ 2 + 3 ^ 3 as well as 20 ^ 2 - 7 ^ 2

e) Anagrams of 153 are 135 and 315 as well and guess what.. 135 is difference of two squares 12 ^ 2 - 3 ^ 2 and 315 is difference of two squares as well 18 ^ 2 - 3 ^ 2!!

Now finally...

f) 153 + 351 gives 504 which is the lowest 3 digit number that has factors from 1 to 9 except 5 

When we multiply 504 with 5 we get the magic number 2520, which is the smallest 4 digit number with factors from 1 to 10. 

One of the anagram of 2520 is 2025 - Our perfect square year!

Welcome 2025 again!

Blog 147: Welcoming 2025!

Received a short note about some interesting facts around the number 2025 through social media channels earlier today and that kindled my spirits to write my next Maths blog welcoming the year 2025 a bit in advance - a number that is pretty unique and versatile and something which we could all relate to when we work as a Team in the corporate world!

 

To begin with here are some straight-forward ones

a) 2025 being a perfect square

b) Product of two squares (81 and 25)

 

I mentioned earlier that 2025 is unique and versatile and has its own standing among 4 digit squares... The square ends with 25 which lends more flavor and diversity when it comes to interesting patterns. It exhibits characteristics that we all look forward to, when we form teams to execute transformational and strategic initiatives

Let's take a look

1. 20 + 25 = 45 and square of 45 is 2025 - A team is made up of different set of individuals who bring together various skills to achieve a common goal!

2. 2025 is square of sum of all digits from 1 to 9 as well as sum of cubes of digits from 1 to 9!!!! One of the anagrams of 2025 is 2520 that shows a similar pattern - it is the lowest 4 digit number that has factors from 1 to 10.

 

3. Add 1000 or 10 ^ 3 to 2025 and we get 3025 which is also a perfect square ending with 25..

Talk about adapting to different situations with seamless ease, wearing multiple hats!

 

4. Remove 0 from 2025 and you still get a perfect square ending with 25 - 225! Deliver similar output with lesser resources...

 

5. Extending the point above - Remove 0 from 2025 and add 64 which is a perfect square to 225. The resultant is 289 which is again a perfect square. Now let's get back to 2025 and add 784 (which is a perfect square) and the resulting number is 2809 - yes it is a perfect square again!

Notice the transition - we removed 0 from 2025 to begin with and finally got 2809 (0 back in the number 289) - A classic case of making different strategic moves throughout the execution phase to arrive at the final destination!

 

6. Prefix a perfect square (4) to 2025 and guess what - We get 42025 which is a perfect square again - Continue to upskill as we move forward in the journey to deliver value!

 

7. 2025 is the only perfect square during the 21st century just like some of its predecessors like 1936, 1849 as well as its successors like 2116, 2209 but what makes it also interesting is it joins the club of these "unique years" whose last 2 digits is a perfect square starting with 1600

 

1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600...

 

Clearly 2025 is versatile, unique and finds its place among a special set of numbers which demonstrate standout behavioral patterns, diverse characteristics and seamlessly adapts itself, as it goes through the transformation journey, while retaining its core attribute all the time of being a "perfect square" year !

 

Wishing everyone a very Happy and Prosperous 2025!

#MathsForFun #Welcome2025

Blog #146: It is all about Maatram

This blog post is dedicated to every Maatram student, Alumni and the core team led by Sujith Kumar. Here we go...

At Maatram Foundation, we had the Alumni annual leadership camp last weekend. It was a great opportunity to get together and connect with an amazing and enthusiastic group of individuals, who are always on the lookout to sharpen their skills and learn something new everyday.

MAATRAM stands for Transformation and let's see how the numbers and digits go through a Transformation below

Each letter of the word MAATRAM when mapped to numbers add upto 67 - 13+1+1+20+18+1+13.

A) 67 is a prime number to begin with and the digits add upto 13 which is again a prime

B) MAATRAM starts with M and ends with M which maps to the number 13 again!

C) MA at the beginning and AM at the end act as a mirror image and flank the three letters in the middle - ATR. A,T, R adds upto 39 which is a multiple of two prime numbers 13 and 3!

D) Prefix numbers 1 to 9 to 67 and this is the pattern we see

    1) 167 - A prime again

    2) 267 - Product of two primes (89 and 3)

    3) 367 - A prime

    4) 467 - A prime

    5) 567 - Product of a perfect square 81 and a prime (7)

    6) 667 - Product of two primes (29 and 23)

    7) 767 - Product of two primes (59 and 13)

    8) 867 - Product of a perfect square 289 and a prime (3)

    9) 967 - A prime!!

The pattern demonstrated above is relatively unique comprising of only primes and squares!

E) And finally MAATRAM means TRANSFORMATION and when Transformation is mapped to numbers and we add those digits (20+18+1+14+19+6+15+18+13+1+20+9+15+14), the resultant is 183 which is again a multiple of two primes! 61 and 3. Not only that, for Indian cricket lovers the number 183 is very special as it was the winning score in the 1983 World Cup victory :)

Clearly the numbers tell the narrative about what MAATRAM stands for. "Prime" reason why our Foundation is very different and strive to bring in a positive transformation in the lives of many students. Extremely glad to be associated with Maatram for more than a decade now, giving back to the student community in the field of education, a noble cause that is very near and dear to me. Looking forward to the next 10 as our Maatram Alumni team gets stronger year by year led by many amazing professionals!

Sujith Kumar, Punitha Anthony, ADITYA SETHURAMAN, Naren Sundram, Rajagopalan R, Vinu Viswanathan, Saravana Subramanian SAFe® SPC, Princely Samuel, Vinoth Kumar, Sarath R

#MaatramFoundation #EducationForAll #Transformation

Blog #145: Welcoming 2024

As we step into a brand New Year, here's a short Mathematical note welcoming 2024

1. 2024 is a difference of two perfect squares - 2025 and 1 and #2 and #3 below illustrates that through alternate means

2. Add digits 1 to 9 and we get 45. (45 + 1) * (45 - 1) is 2024

3. Add the cubes of the digits from 1 to 9 and the resultant is 2025  (45 ^ 2). Subtract 1 ^ 2 as in #1 and we get 2024 again!

4. 2024 is also sum of 1936 + 88. In turn 1936 is nothing but a perfect square of 44. 

Hence 2024 can be written as (44 ^ 2) + (44 * 2). Look at how 2 and 4 which are the primary digits that make up 2024 come into play again! Add 20 and 24 and the resultant is 44 again!

5. Last but not the least..2024 x 2024 = 4096,576 where 4096 is a perfect square and 576 is also a perfect square (24 in action again!)

Wishing everyone a very Happy, Healthy and Prosperous 2024!