"Sir, tomorrow is a Happy Date"

Do you know that we had an interesting mathematically special date few days back. Yes, it was 28th June. To be honest, I had missed this observation, and got informed about this via facebook or whatsapp, only on the other day....  But I grabbed this opportunity to talk about this with my students. 

I asked them on the next day "Can you figure out something interesting in yesterday's date?"

( Check this link to read the entire post: http://rupeshgesota.blogspot.in/2016/07/sir-tomorrow-is-happy-date.html )

To be honest, I was NOT expecting the correct response. Why? 

Not because I don't trust them. But because we had just touched upon this category of numbers, and that too around 5-6 months back, and had never visited that territory again. 

But you know what? Kanchan shocked me. And I am so happy that she proved me wrong!

"Sir...... both 28 and 6 are Perfect Numbers! "

Super !! Isn't it ? 

(Well, you will probably appreciate this more if I tell you that this girl is from a Class-6 municipal school, with no facilities,  privileges and parental support in her 100 sq. feet home situated deep within slums. And how about asking this question to a bunch of students from posh background?)

Perfect number is a  positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. 

I wanted to write a separate detailed post on this particular class on perfect numbers, because we did a host of interesting things on this day... 

How do I know if that was 'interesting'?  ..... Because ALL my students founded it very very interesting.. There were many Oooooohs and Aaaaaahs in our class..... Many eyes and mouths were seen wide open.......... :-)

Here is a snapshot of 'only part of the stuff' that we did on that day.. (Thanks to the 'Perfect Date' :)   

Don't get scared if you are alien to some of the terms on the board.... Either you may google for it.... Or how about visiting my students some day and learning from them ?  :-)

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Hmmm..... Now when the background is set, lets begin the real story ! 

Something More interesting happened yesterday....

Can you guess??   :-)

"Sir, tomorrow is Happy Date !! "

And this time, it was like..... me with my eyes and mouth wide open :-)

"7th July....    Both - the date as well as month - are 'Happy Numbers'......"

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers)...For example, 19 is happy, as the associated sequence is:

1² + 9² = 82

8² + 2² = 68

6² + 8² = 100

1² + 0² + 0² = 1.

"Wow... I am so glad you could spot this... But how did you spot it ?"

"Sir, we were waiting for this date, since the day we discussed about 'Perfect Date' "

It was a Sixer !!  I had no words for their growing mathematical dedication. 

But the Math Teacher in me soon woke up -- "Hey, but what about the year 2016?"

"No sir, that's not a happy one... We checked it.", with a little unhappy face :-(

I thought for a while...... "Ok.. So Can we then know, what's the next nearest happy date?"

"Sir, you mean, even the year?"

"yes dear!"  :-)

We had just unlocked the door of our class while we were chatting about all this, without even being seated..... But this probing question pushed them to their seats immediately,... some started doing the number crunching - mentally - on their own, while others started working on this with their peers....  And in no time, there came a loud voice....

"Sir, I got it !!"

"Hey wait... Hold on....Lets give 2 more minutes for others."

Hands started going up one after the other..... 

I really didn't care much about the Happy Date at that instant..... what made me Happy was their Happy Faces and the Happy environment :)

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Can you figure out the date on your own without scrolling down for the answer?    :-))  .
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Hey, no cheating :)
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Got it?
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If you have got 1st January 2019, then you are correct !!

Student-1: "Sir, it is too far... We have to wait for THREE years!"

Student-2: "... We will be in Tenth standard in 2019"

Student-1: " Yeah..........  But We can be Happy in Tenth std. only if we get good marks"

Student-3: " Listen..... Even 10 is a Happy number... So we can be Happy in Class-10 even if we don't get good marks!"

:-)  :-)   :-)   :-)  :-) 

Student-4: "We can be Happy this year too.... We are in Class - 7 !!"

:-)   :-)    :-)     :-)   :-)


Regards

Rupesh Gesota
www.supportmentor.weebly.com