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.
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.
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
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.
kasam se yar... kya class tha!
Whoever watch the first Video will fall in love with This..Well explain Thank you sir
Excellent explanation dear sir. Really awesome
Thank you so much sir you teach me a new thing
THE best explanation I have come across among other channels
Brilliant knowledge you have sir thank you so much
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.
Big fan of you sir
Best explanation sir💐
Very good and useful, I am an army commander in the midst of your fellow 193k subs :D
please also do of rectangles
Please solve more difficult questions in counting triangles
So good explanation Sir!!
Thanks Sir...😊
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
I seen so many classes but my doubt is clarify in this video only thank your sir and your teaching is awesome❤️❤️❤️
Can't say anything more than thankyou ;-)
Thank you so much sir for your excellent explanation
Thank u Sir . Im so weak in reasoning plis update more videos
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!
Thank u sir .. It helped me a lot
Thankyou sir 😭🙏
The best...
Thank you so much sir , for such a fantastic explenation.
Excellent explanation!
Super sir meru
Hare Krishna hare Krishna Krishna Krishna hare hare
Hare ram hare ram ram ram hare hare
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.
Thank you So much Teacher is it ok when I call you teacher
Thank you sir🥰🙏
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
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
Very nice trick Sir 👌🏻😊👍🏻
Thanks. Do share the links with your WhatsApp groups and contacts
Thanks a lot sir.. This is so helpful. I'm preparing for ntse exam 😁❤
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 )
Very well explained video sirji....all d qstns are too gud..
For pdfs of short tricks WhatsApp 9896369963
The 10:56 part is it not 5 instead of 4?
Sum((n^2+2((n^2)-n)+abs(cos(n*pi/2))),n,1,s) where s is the side length of the squre
Tq u sir
Nice trick
Tussi great hooo😃😃
Thank you sir :)
Sirr thnkuu.. Such understanding 🙏🙏🙏🙏
Thanks u sir voice very nice sir
Awesome sir
Dil se prnam
Sir, I think last question ans:53...
Agar sir ek side 3 ek 4 ho to
Thank you sir
Lovely
Very nice lecture sir thanq
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
Sir please can you also make a video on rectangular number with formula
Yes sir
Thank. U sir.help alot
Nice sir
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.
Nice concept
thank u
Amazing
👍👍
Sir there is one another dig. Plz solve it 🙏
Thank you so much sir
good
Thank you sir....
E by 3 Ka batao
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 🙂👍 😀🙂👍
Mera bi 1 question hai Sir
Thank u sir, your super, amaginig exaplanation
Sir, agar isi figure me no. Of triangle batane ho tab kya trick hogi
I belong to hindi medium bt I try understand nd I got it
Good you can teach but next time use colored pens and you'll be ok
Beautifully explained 👏🏻
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 )
very good. even i have my youtube channel on maths tricks..named "maths scam"
Why not concepr sir ; trick is nothong but excuse for learning
We need Triangle tricky way method Sir????
Do share the links with your WhatsApp groups and contacts
Thank you so much sir!
Oru dout , if we got only two Column and 7 rows how to solve it
7*2+7*1= 14+7= 21
Pls say proof
Last one 25 square...I think.. not 23... Please reply me...23 or 25?
It is 23
Sir Hindi m
😀
Bad
Tamil la solluga sir
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