Author: nmbrguy

2022 in Roman numerals is MMXXII.  It is one of only four numbers whose Roman numeral equivalents have the pattern — aabbcc

222 AD was the last time a year had this pattern: 222 in Roman numerals is CCXXII. Next ones will be 2202 (MMCCII) and 2220 (MMCCXX)

Another piece of trivia: 20th Feb 2022, in US notation, is a palindrome in Roman numerals — II/XX/MMXXII.  20th Feb 222 AD was one too (II/XX/CCXXII)

As we step into this somewhat uniquely numbered year, here’s wishing you and your family a Very Happy Healthy Peaceful and Prosperous New Year 2022 !!!

–nmbrguy!

A couple of months back, during an Ola ride, I spotted the number 6592 in the number plate of an oncoming car.

I promptly went about one of my usual mental computing activities — that of multiplying the two 2-digit halves that make up a 4-digit number.

In this case, multiplying 65 and 92.

Extracting 13 from the 65, and 23 from the 92, their product 299 flashed. Without waiting to consider the remaining multiplicands (5 and 4, respectively) I doubled 299 to get 598, affixed a 0 and obtained 5980, as the product of 65 and 92.

5980 … the number seemed familiar. Indeed it’s from the number plate of my childhood friend’s family car, from nearly 4 decades ago. (I checked with him to confirm 🙂 )

From car to car, the number circle was complete!

Today is the 13th of August ’21, and in the US style, it is 8/13/’21.

The three numbers are ascending consecutive Fibonacci numbers.

This is the last occurrence in this century of such a date with ascending consecutive Fibonacci numbers.

If you are not happy with ’21, and want a real Fibonacci year, you’ll have to wait until 2584, but that won’t feature in a date like 8/13/’21 with ascending consecutive Fibonacci numbers.

On my way to work on 19 Sep 2019 I saw the number 8257 …

Instantaneously, it was split into four squares in the following way:

• First 8100 (90**2) appeared, leaving 157
• Almost in parallel, 144 (12**2) emerged from 157 leaving 13 (which is 2**2 + 3**2)

It felt like the brain was on autopilot while splitting 8257 as the sum of the squares of 2, 3, 12 and 90.

After typing up the above stuff, it struck me as to why the number 8257 appeared so familiar …. Intel 8257 is a DMA Controller chip from the mid-to-late 1980s and was part of my undergrad CSE curriculum!

Continuing to be intrigued by how the brain works …..

–nmbrguy!

Identifying patterns in numbers that I come across in daily life, as well as performing mental arithmetic on them — these are continual threads of activity that run in my mind.

For example …

1. 1. I might recognize that a 3-digit or 4-digit number I notice is a 4th power, or
   2. I might split an observed 4-digit number as the sum of 4 squares.

Now the first one involves a simple one-step action— I know the first dozen or so 4th powers, so it’s just a memory lookup.

The second one is a bit more involved.   It involves an assortment of simple steps — lookups, additions, subtractions, etc.  In any case, most of the steps are not automatic, but are executed in a deliberate and consciously-performed manner.

The other day, however, something intriguing happened …

I was returning home from work when I spotted, in a vehicle’s license plate , the number 6264.

The very next instant the number 3968 flashed in my mind.  It was surreal.

I set out to analyze the relationship between the two numbers that led to the second one’s appearance upon noticing the first.

Here’s what I think happened in my mind from the time I spotted 6264 until the next instant when 3968 flashed.

1. 1. 6264 spotted
   2. Split midway into 62 and 64
   3. 62 x 64
   4. (63 – 1) x (63 + 1)
   5. 63² – 1²
   6. 3969 – 1
   7. 3968 flashed

Steps 2 to 6 happened subconsciously.

Perhaps such subconscious computing has occurred in my past, but this was an instance that made me sit up and left me yet again in amazement at how the human brain works.

–nmbrguy!

In this short blog I’ll mention a couple of immediate thoughts on the new year number 2017.  Feel free to add your thoughts below.

From a number property perspective, it’s cool to note 2017 is prime!  The previous prime number year was 2011 and the next is 2027.

Being a prime number of the form 4n + 1, 2017 is expressible as the sum of two squares in exactly one way: 9² + 44². For more details on representing numbers as the sum of two squares, see, for example, this Wikipedia link.

From a calendar perspective, 2017’s Doomsday is Tuesday. This means, the following dates in 2017 fall on a Tuesday: 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7, pi-day (3/14 in the US) and the last day of February. For more details on Doomsday, see this Wikipedia link.

Here’s wishing you a Happy, Healthy, Prosperous and Peaceful New Year 2017.

–nmbrguy!