Intuition for why the sum of squares works: n^2 = number of 1x1 squares that can be counted (n-1)^2 = number of 2x2 squares that can be counted. Visually, just think of this as removing the top row and right column, then treat each remaining square as the bottom-left square of your 2x2 grid. Then since every square in the (n-1)^2 grid represents the bottom-left of every 2x2 possible, there must be (n-1)^2 such 2x2 squares possible. Same thing for (n-2)^2 and onwards, just remove the next top row, the next right column, treat every remaining square as the bottom-left of a 3x3 grid. This applies to the rectangle case as well.
Respected Sir, I have a query regarding the figure in which you counted 30 squares. you calculated 4*4=16 3*3=9 2*2=4 1*1=1 total stands 30 now my query is that if we hide all 30 squares then in the last 1 more big square remains. This big square which contents all 30 squares. but in counting whether we should not add big square that is 30+1=31 square. I hope you understand my query. waiting for your reply sir
My question is on the one we counted 72 squares. The first 30 is fine then the next 30 then the next 8. But my concern is for the last 4 squares. Is it not supposed to be 5 instead? Because of the middle part.
Sir can you make a new playlist I mean a whole series of .. videos for NTSE MAT as it's coming soon ... ( I mean sir please make a series of evey topics as you know a lot of tricks )
In the last question , the final 3 squares that yiu added doesnt seem like squares. They are parallelograns . ( Equal lengths but the angles ate not right angles )
This is a good lesson. However, if you had used colored pens when changing squares and/or shading, it would have made it clearer.
Whoever watch the first Video will fall in love with This..Well explain Thank you sir
Intuition for why the sum of squares works:
n^2 = number of 1x1 squares that can be counted
(n-1)^2 = number of 2x2 squares that can be counted. Visually, just think of this as removing the top row and right column, then treat each remaining square as the bottom-left square of your 2x2 grid. Then since every square in the (n-1)^2 grid represents the bottom-left of every 2x2 possible, there must be (n-1)^2 such 2x2 squares possible.
Same thing for (n-2)^2 and onwards, just remove the next top row, the next right column, treat every remaining square as the bottom-left of a 3x3 grid.
This applies to the rectangle case as well.
thanks for the comment.
THE best explanation I have come across among other channels
Excellent explanation dear sir. Really awesome
kasam se yar... kya class tha!
Please solve more difficult questions in counting triangles
I seen so many classes but my doubt is clarify in this video only thank your sir and your teaching is awesome❤️❤️❤️
Brilliant knowledge you have sir thank you so much
Sir im super thanks to you.your class make me deep thinking and undstnd from yur trick and method which i had never heard and known before
Do share the links with your WhatsApp groups and contacts
Thank you so much sir you teach me a new thing
So good explanation Sir!!
Thank u Sir . Im so weak in reasoning plis update more videos
Hare Krishna hare Krishna Krishna Krishna hare hare
Hare ram hare ram ram ram hare hare
Respected Sir,
I have a query regarding the figure in which you counted 30 squares.
you calculated
4*4=16
3*3=9
2*2=4
1*1=1
total stands 30
now my query is that if we hide all 30 squares then in the last 1 more big square remains. This big square which contents all 30 squares.
but in counting whether we should not add big square that is 30+1=31 square. I hope you understand my query.
waiting for your reply sir
This big square is already included in 30 total squares,dear learner yar
Very good and useful, I am an army commander in the midst of your fellow 193k subs :D
My question is on the one we counted 72 squares. The first 30 is fine then the next 30 then the next 8. But my concern is for the last 4 squares. Is it not supposed to be 5 instead? Because of the middle part.
Yes I am also having same doubt .
Yes .l have a clarity on that.the centre square is counted in second 30. Observe it carefully
thank u sir.....clear pronounciation and explanation!
Can't say anything more than thankyou ;-)
Best explanation sir💐
Thank you sir,, its an amazing trick.. Lots of best wishes from pak.
Thanks. Do share the links with your WhatsApp groups and contacts in Pak
Dear Sir, In Tricks 415 shortcut 13 the total number of squares comes to 54 and not 50. Please check and correct. Thanks. Please respond.
Thanks a lot sir.. This is so helpful. I'm preparing for ntse exam 😁❤
Big fan of you sir
Thank you so much sir for your excellent explanation
Sir can you make a new playlist I mean a whole series of .. videos for NTSE MAT as it's coming soon ... ( I mean sir please make a series of evey topics as you know a lot of tricks )
Excellent explanation!
Thank u sir .. It helped me a lot
Thanks Sir...😊
Thank you so much sir , for such a fantastic explenation.
please also do of rectangles
Sum((n^2+2((n^2)-n)+abs(cos(n*pi/2))),n,1,s) where s is the side length of the squre
Very well explained video sirji....all d qstns are too gud..
For pdfs of short tricks WhatsApp 9896369963
Thank you So much Teacher is it ok when I call you teacher
Super sir meru
The best...
Thankyou sir 😭🙏
Sir, I think last question ans:53...
Very nice trick Sir 👌🏻😊👍🏻
Thanks. Do share the links with your WhatsApp groups and contacts
Thank you sir🥰🙏
Thanks u sir voice very nice sir
Agar sir ek side 3 ek 4 ho to
Awesome sir
Dil se prnam
Thank you sir :)
Nice trick
The 10:56 part is it not 5 instead of 4?
Sir please can you also make a video on rectangular number with formula
Yes sir
Tussi great hooo😃😃
Very nice lecture sir thanq
Thank you sir
Tq u sir
Sir there is one another dig. Plz solve it 🙏
Sirr thnkuu.. Such understanding 🙏🙏🙏🙏
Hello sir.
Have you taught Mathematics at Army School (Army Public school), Ambala Cantt.
Of course yes
@@sureshaggarwal Sir, what a small world it is. You have taught me when I was in 8th grade (2006-2007). It is so good to see you.
If we are asked to find number of triangles from the figure shortcut 12 what is the trick? Please can u help me
Ur great sir
I don't know you I am not your student i am just a 10year old girl but I am very Happy with you uncle be safe be in home 🏡 be happy be healthy 🙂👍 😀🙂👍
Thank you so much sir
I belong to hindi medium bt I try understand nd I got it
Thank you sir....
Nice concept
Nice sir
Beautifully explained 👏🏻
Thank. U sir.help alot
Mera bi 1 question hai Sir
Lovely
thank u
👍👍
Good you can teach but next time use colored pens and you'll be ok
Amazing
Why not concepr sir ; trick is nothong but excuse for learning
Sir, agar isi figure me no. Of triangle batane ho tab kya trick hogi
Thank u sir, your super, amaginig exaplanation
E by 3 Ka batao
good
very good. even i have my youtube channel on maths tricks..named "maths scam"
We need Triangle tricky way method Sir????
Do share the links with your WhatsApp groups and contacts
Thank you so much sir!
In the last question , the final 3 squares that yiu added doesnt seem like squares. They are parallelograns . ( Equal lengths but the angles ate not right angles )
Tamil la solluga sir
Pls say proof
Sir Hindi m
Oru dout , if we got only two Column and 7 rows how to solve it
7*2+7*1= 14+7= 21
Last one 25 square...I think.. not 23... Please reply me...23 or 25?
It is 23
😀
Bad
Can do better
Thank you so much sir
Super sir
Thank you sir
Thanks sirrr
Thank you sir...
Thanks sir ..
Thanku sir ..
Thanks sir
Thank you Sir
Thank you sir
Thank you Sir
Thank u sir