Tuesday, April 3, 2018

An interesting date today :)

"Sir, tomorrow is an interesting day!", my students drew my attention to an old post-it note stuck on our notice board.

"Oh, really? And what's that?"

"Its 4th day of the 4th month (April), and its also falling on the 4th day of the week i.e. Wednesday."

Flash back - we had figured out this special day many months back, but I could not recollect the specific instance that had triggered us for this exploration.So I asked them.

"What had made us landed up on this?"

It did not take much time for them to recall - 

"Some one had given you the problem last year that if 1st January 2017 falls on Sunday, then 1st of which month will be Sunday again? While working on its solution, we had extended that problem to this present one..."

"Oh yes...!"

Then I thought if the year 2018 too could give us a 4 in some way. I tried for a while, but in vain.I shared my disappointment with them.

Probably, one of my students, Kanchan, took this seriously and almost within couple of minutes, came up with this marvel:

I hope you will spare at least half a minute to appreciate the beauty of this expression. No doubt I could notice several interesting properties in this, however, the villian in me pushed the student to explain everything :)

And here she goes -
1) The digits of the year 2018 are used in order.
2) Each digit has an exponent
3) Exponents too are in order (descending as well as consecutive).

And this was her final stroke, which I had failed to notice -

4) The expression evaluates to 4.

Yes, it was a 4 again... She used the year 2018 beautifully to yield a 4, which her teacher had failed to do. Now, isn't that a proud moment for a teacher?  :-)

---  Did you figure out all these interesting properties?

---  And if this is not enough to delight you, let me also tell you that my students have also figured out the next immediate date which has similar interesting property like 4th April 2018 (falling on the 4th day of the week). Can you find out this date? And probably even next date after that?  i.e. Xth day of Xth month which falls on the Xth day of the week. 

--- How about doing this activity with your students?

Do let me know your views and experiences about this.. Will be eager to know...

Rupesh Gesota

PS: Students belong to marathi medium government school (class-7 and 8) based at Navi-Mumbai.  They hail from disadvantaged backgrounds. To know more about their Maths Enrichment program, check this link: www.supportmentor.weebly.com

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