How To Solve This Maths Olympiad Problem ? | Aman Malik Sir
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- เผยแพร่เมื่อ 7 ม.ค. 2025
- This question is picked from regional maths olympiad
(666....6)^2 + (888....8) = ?
Given that the number of digits of 6 and 8 are 100 each in both the given expressions.
Solving Olympiad problems builds your question solving approach
This is a very interesting question from Maths Olympiad which will surely test your critical thinking skills.
Solving such questions will also train your mind to open up and go for in-depth and out of the box thinking.
Stay tuned with @BHANNATMATHS for more such interesting questions.
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#maths #mathematics #olympiads #amansirmaths #jee #jeemains #iitjee #jeeadvanced #olympiadmath #mathsolympiad
Bahut beautiful question hai
This question gives us an inspiration that we should look at all the calculations according to the point of view of series .Indeed this is a fantastic calculation. Sir !
6^2+8=
66^2+88=
666^2+888=
I asked Chatgpt to simplify these three terms, because i sensed there could be a pattern. Indeed there is.
I use chatgpt because i appeared in IIT-JEE/AIEEE in 2007 and 2008
Buddhe
A beautiful question and it's visualisation of numbers ... mind blowing sir
Sir, I solved a little bit different if I take 111...1 (100 times) = x then we can rewrite the sum as (36x^2+ 8x) = 4x((9x+1)+1) ( iwrote 9x+2 as this because it gives advantage when 9x+1 is written it becomes 1000...0(100 times 0s) and then the question is easy and simple manipulation gives result 444...4(200 times 4s)
Yus but mera 44444 201 times aaya ese
@@Stockjunonope bro if you take 444× 1001 = 444444 like that you get 200 when you multiply (1000(with100times0) +1) I think this is where u got confused
Still I have easier solution
Another great problem explained by a great teacher
Beautiful PATTERNS and beautiful question
Sir is question ko kaise solve krsakte hai?
Limit x → 0 (x^x^x^x^.... n times)
Is par ek video bana dijiye
And agar aapke paas power tower k concept pe koi aur questions bhi hai to uspar bhi video laiyye
Respect for Aman sir ❤
East or west, aman sir is the best
Sir app to maths ke GOD ho,
Apko mera pranam 🙏🙏🙏🙏🙏🙏
Lovely..
Wonderful sir..long live
One more way of doing this can be - 66^2 = 4356, 666^2 = 443556 and so on. Hence 6666666...100 times^2 = 44...99 times355... 99 times6. And if we add 888...100 times to this the answer will quite visibly be 444...200 times
Yeah bro! But it is lengthy aa we have first calculate the squares of 66,666 to recognise the pattern
I also solve like this why .. and it is also not much lengthy justa little multiplication thing
only one channel in youtube , that makes us creative , seriously 😎
I just Did 6²+8 = 44 , 66² + 88 = 4444 and Got Answer 🙃 JEE walo ka Jugaad ❤
same it took me 10 sec lol
How you put this sum please explain me
@@balasubramanianmanickam3067 in question there's 100 times 6666.. and 888..... , Just take 6² and 8 1 time u will notice pattern ie 44 4444 444444 etc
@@chirantan69iitb first of all thank for your explanation could you elobrote the explanation
@@chirantan69iitbRAM RAM JI 🚩❤
Nicely explained 😊
Ye to sequence and series se nikal jayega, inn numbers ko expand karke 1×10².... Karte karte expand kardo, fir GP ka sum laga do aur square kardo first num ko and second wale me add kardo.... it's that simple 😊
Sir ye jo apne last me trick bataya wo sabhi numbers par apply hoga kya sir ya fir 6 and 8 ke case me hi apply hoga
Please it's my last doubt😢😢
Thank you sir❤❤
Maine general analysis se solve kar liya
Pehle i checked 6^2+8=44 isme 6 aur 8 ke 1 digit the aur answer 44 aya 2 digit ka
Fir maine dekha (66)^2 +88 iska value aaya 4444 aur isme 6 aur 8 ke do digit the aur answer 4444 aya jisme 4 digit hai
Agar is sequence ko analyze kare tab (666...100times)^2 +(888...100 times) ka answer (44444....2×100times) ayega.
Aise questions me itna lamba solve karna (jaise sir ne kiya) buddhimani nhi hai balki apna general thought process se karna eak bahut hi better option hai this saves a lot of time
What you did is good in exam. But in practice one must know the real solution as well.
Even sir did your analysis in the end.
that's not how math works , have you ever heard about moser's circle problem ? if not, then you should go and check you will get my point.
Beauty of mathematics 🎉❤☺😍
ye question humare class mai karaya gaya tha sequence and series chapter mai
Amazing question!
i did this question by long way take common 6 and 8 respectively. further taken 11...1, 100 times common from both expression and by observing pattern i got an expresssion like[11111....1]100 times multiply with [100...01] 101times and got[444....4]200times.
Amazing sir keep this series always
Very nice 👍 Thanks.
I respect you sir❤❤❤ your teaching style
beauty of every Olympiad problem is even though they would be solved by using maths and all but they all have a pattern or series to get the answerr without much calculation means just by observing the problem like sir explained in the last.
Sir from 666... I take 6 common and multiply and divide by 9 than it gives 6/9 times( 10 ki power 101 minus 1) than similarly solving 8 like this my answer is coming 4 201 times
Sir what is the mistake in my solution
Sir please explain it
sir i opened (6666...6)^2 and added it to (888...8) and got answer in 3 micro seconds😀👍
Best math teacher I have ever seen in my entire life. ❤❤❤❤❤❤
gb sir se padhe ni ho bhai
sir jiiii maaza aa gaya ...love from odisha
200 or 199 as subtracting one from 10^anything reduces digit count by 1
I was wondering the same, but the number is 1 and 200 zeros. So it is a 201 digits number. After substraction it is a 200 digits number. For example 10²-1=99.
If we take 4/9(10**100-1)common then after rearranging it will be in the a**2-b**2 format And it will be more easy
Sir (6(10*100+10*99..........10*0))*2
Aisa karke phir GP ke sum ka formula laga De similarly 8 wale ke like bhi aisa kare to answer aa raha hai
Sir m to log lekr kr rha tha aur kahi aur hi pahuch gya 😂
Fantastic 🎉
Sir what a teacher you are
Aaj pahali bar apaka solution dekhe bina mujhase ye question ban gaya.
Apane ek Barr kaha tha sir ki Pattern pakadana seekho question ka. Aur is Barr mai pakad le gaya😊
Very nice problem and beautifully explained
Two functions ka product ka kise graph mein plot kar sakte hai
Ushka video bhi le aayie
Example-x/sinx
Sir please solve jee main pyq from2019 to 2023 with short tricks jee advanced 2013 to 2023
The problem with the Indian education system is that they don't tell you if there is a practical application in trying to solve this question, if there is any
I gave this answer by using mathematical induction
Bohot mast qs tha maja aa gaya ❤❤
Maza aagyya sir mjhe to pehle laga isme to kuch 12th ka hi funda laga hoga but mai 11th me hokar bhi samajh paya kyunki mmaine thodi si gp padhi thi love it
Sir, please ye question solve karke dikhao. (Ye maine khud banaya hai)
A^3 - B^4 = C^2
And A+B=C
Find A, B, C
Sir last me Jo pattern bataya wo mazedar laga
Nice problem,thanks
3:58
If we also take 10^(100)-1 common, it will be more easy
BTW, thanks for this amazing problem
Greatest Approach
Best math teacher ever
As we all know,
6*6=36
66*66=4356
666*666=443556
6666*6666=44435556
66666*66666=4444355556
Means for n no 6 digit number squared itself the product comes (n-1) time 4-3-(n-1) time 5-6
So that mean (66666...66666(100 times)) ^2 =(99times4-3-99times5-6)
Here this is 200 digit no so if we all 100 digit 8s i.e. (88888...88888(100times))
Means
44444...44355555...55556
+ 888888...88888
=4444...4444444...44444
(200 times)
~4.4444...(199 digit) *10^199
❤
👍
444...4 (200 times) my answer
Sir I am in 9 class and have also solved this in first attempt but without using geometric progression
I did it myself but I am in 10th and used the formula of sum of Finite GP from google
Oh, really good, keep learning and trying, god bless you
@@aasarfilal3021 thanks 👍
This question is also in Esaral jee module...
Thoughness
sir aaram se solve ho gya love u 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444
Sir 2 last step mey kya binomial theorem laga sakta hu?
Sir x^x^x^....infinity=2 and x^x^x^..... infinity=4 both have same answer as root 2,how it is possible can you explain please
a/9(10^n-1)❤❤
Sachin sir 😅
Hehe 😂❤
Solved in the first try
But didn't use GP just opened the series and took 4×111.....1 common and simplified it
Lol same here
What about 1/10-1
sir almost same question appeared in jee advanced 2023 there also a gp was formed and the question was solved...by the way
sir you are the best
I am from Brazil.
Let do it for n digits, in stead tô 100.
[6*(10^n-1)/9]^2+8*(10^n-1)/9=
4*(10^2n-2*10^n+1)/9+4*(2*10^n-2)
=4*(10^2n-1)/9
This is a number with 2*n digits 4 in decimal numbers.
As n=100
x=444..444 with 200 digits
Nice problem.
Very interesting sir, love from bihar
Very good sirji
Solved in first try and 3 minutes. Very easy
Simple gp problem
Sir please aap aise question lekar aavo🎉
What will be the answer if there is square of 888....8 also ie (888.... 8)^2?
JEE advanced 2023 mein aisa hi ek question thaaa
Amazing pattern is mind blowing
I did it myself I love sequences and series thanks sir
sir kya is problem mein gp ka concept laga sakte hai kya
Good question
Sir ek help kar doge
Sir ek assi video banado jismai particular topic or chapter par 100 ya 200 questions ho Taki wo chapter ya topic ache se AA jaye
sir i am facing problem in solving modulus function questions ... please suggest me something
Excellent
O sir i m you big fan and today first , just i think like your second method and then find the final answer is 444....200times
L❤ve y❤u sir.
Sir ki, bohot Maja aya❤❤
This concept also asked in jee advanced 2023
Great sir
Sir what is the place value thing
Sir, I also got the answer // it was same as your 2nd method ☺❤
Sir aapke lectures abhi bhi pw app par available hai🙂🙂...
Zabardast!
this type of question appear my 11th half yearly i am serious but that was 6+66+666+6666........... they both seem similiar this can be done by taking 6 coomon an d multiply by 9 and writwe 9 as 10-1
Sir this is a problem of S.N Dey math book which is avilable in English
4444.... 200 times😊🎉❤👍
Great
Sir maza aagaya ❤❤❤❤❤
you are drawing the system icon incorrectly. he is upside down
This question is in cengage algebra exercise 5.5
Sir ham isko alag tarike se kiye hai or ose bahot ashani se or bahot khubsurti se hoa hai
Amazing 😍
Very beautiful... bus ek hi baat hai, Don ko pakadne se v mushkil hai screenshot lena, speed slow karke o to le liya, aage aisa khubsurat sawal ke intezaar....
Op question dil cho gaya ❤
Sir, I am solve this question without see your answer i am solve this very simple method how I you show my solution sir ..
Bawal sawal....❤