Blog Post #115: The curious case of Zip codes!

This blog is dedicated to everyone at Mr Cooper and some fun using Maths to show the close collaboration across US and India offices!

US Corporate office Zip code at Coppell, TX is 75019

India Corporate office Zip code at Chennai, TN is 600089

Let's look at some striking similarities

a) Digits of 75019 adds up to 22 while that of 600089 adds upto 23 - These are like thick pals next door!

b) Both 75019 and 600089 are not prime numbers and more importantly number 7 is a common factor for both!

75019 - 1531 * 7 * 7
600089 - 1453 * 59 * 7

c) Now closely look at the first factor for both numbers in the earlier step - 1531 and 1453. Difference is 78 which is a multiple of 13. Now look at the second factor - 7 and 59 - Difference is 52 which is again a multiple of 13! That's incredible :)

d) 750 + 19 (first 3 digits + last 2 digits) is 769 which is a prime
     6000 + 89 (first 4 digits + last 2 digits) is 6089 which is also a prime!

e) 750 - 19 is 731 which is a product of two primes (17 * 43)
    6000 - 89 is 5911 which is again a product of two primes (23 * 257)

The similarities exhibited by these two numbers are amazing to see and truly reflects the collaboration between the teams at these locations!

I am sure if I extend this to some of our other sites in US and India, we will see more such patterns

Blog Post #114: All roads lead to Armstrong number!

This post is around working towards a common team goal and the path that we take to achieve that - have made an attempt to explain that through Armstrong numbers

Let's start this blog listing out the Armstrong numbers that most of us know about - 0, 1, 153, 370, 371 and 407 (Sum of the cubes of the digits equal to the number)

Now let's take a random number say 504 and add up the cubes of the digits till we get to see what happens after few steps!

Step 1:            5 ^ 3 + 0 ^ 3 + 4^ 3 = 189

Step 2:            1 ^ 3 + 8 ^ 3 + 9 ^ 3 = 1242

Step 3:            1 ^ 3 + 2 ^ 3 + 4 ^ 3 + 2 ^ 3 = 81

Step 4:            8 ^ 3 + 1 ^ 3 = 513

Step 5:            5 ^ 3 + 1 ^ 3 + 3 ^ 3 = 153!!

153 is an Armstrong number and the iteration stops here!!! That's sheer magic - Isn't it?

Let's take another number 841

Step 1:            8 ^ 3 + 4 ^ 3 + 1 ^ 3 = 577

Step 2:            5 ^ 3 + 7 ^ 3 + 7 ^ 3 = 811

Step 3:            8 ^ 3 + 1 ^ 3 + 1 ^ 3 = 514

Step 4:            5 ^ 3 + 1 ^ 3 + 4 ^ 3 = 190

Step 5:            1 ^ 3 + 9 ^ 3 + 0 ^ 3 = 730

Step 6:            7 ^ 3 + 3 ^ 3 + 0 ^ 3 = 370

370 is an Armstrong number and iteration stops here!!

Moral of the story

When we work as a team to deliver an outcome, we all strive towards a common goal (which is the Armstrong number in this case) though the paths we take may sometime differ (as we saw in the two examples above)

Not all numbers behave this way but it is an interesting exercise to see which ones follow this pattern!