Please edit it...nafistiham wrote: $ (A+Z)+$$2(B+C+D+........Y)$$=325 $
$ \Rightarrow (A+Z)+$$2{(B+C)+(D+E)+(F+G)+......(X+Y)}$$=325 $
I used the same approach except for the part of generalizing the equations.
Some problems to solve
Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
I used the same approach except for the part of generalizing the equations.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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nafistiham
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Re: Some problems to solve
done.
thanks,vya.i used just "{}".that's why it didn't work.
thanks,vya.i used just "{}".that's why it didn't work.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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Abdul Muntakim Rafi
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Re: Some problems to solve
Labib, we need a way to solve $3$... How can we be sure that these two are the only possible answers...
Man himself is the master of his fate...
Re: Some problems to solve
Use the rules of $a^3+b^3 $ and $a^3-b^3$ (I think a part requires $(x+y)^3-1^3$)
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Re: Some problems to solve
That way directly yields $x+y=1$ or $x-1=y-1=0$
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Abdul Muntakim Rafi
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- Location:bangladesh,the earth,milkyway,local group.
Re: Some problems to solve
Mahi... Can you please elaborate your answer? I didn't understand...
Man himself is the master of his fate...
Re: Some problems to solve
(1,0), and (0,1) are the another solutions for the problem 3.
Re: Some problems to solve
কেউ কি বগুরার ২০১১ এর HSC ০৪ নাম্বারটা সল্ভ করতে পারছ। সোজা জিনিস কিন্তু দসমিক সংখ্যা কিভাবে বাইনারিতে নেব সেটা বুঝতেসি না। উদাহরন আবশ্যক। 
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
Re: Some problems to solve
Here's a conversation between me and DJ which might help.
Me::ডিজে...
"$.1$ পৌনপনিক কে বাইনারীতে কি লিখে?? ঃ-s"
DJ::
"$0.0(0011)$ বন্ধনীর ভেতর পুনঃপৌণিক।"
Me::
"মাথার উপর দিয়ে গেল
একটু ব্যাখ্যা দাও না!"
DJ::
"$0.1$ পৌণপৌণিক $= 1/9 = (2^-4 + 2^-5) + (2^-8 + 2^-9) + (2^-12 + 2^-13) + (2^-16 + 2^-17) + .....$"
@Joty
শুধু $1$ যোগ করলেই পারো।
তবে আমার মনে হয়, উত্তর ১০ হতে পারে যদি তুমি $.9999999999999...=1$ এর মতো চিন্তা করো।
Me::ডিজে...
"$.1$ পৌনপনিক কে বাইনারীতে কি লিখে?? ঃ-s"
DJ::
"$0.0(0011)$ বন্ধনীর ভেতর পুনঃপৌণিক।"
Me::
"মাথার উপর দিয়ে গেল
একটু ব্যাখ্যা দাও না!"
DJ::
"$0.1$ পৌণপৌণিক $= 1/9 = (2^-4 + 2^-5) + (2^-8 + 2^-9) + (2^-12 + 2^-13) + (2^-16 + 2^-17) + .....$"
@Joty
শুধু $1$ যোগ করলেই পারো।
তবে আমার মনে হয়, উত্তর ১০ হতে পারে যদি তুমি $.9999999999999...=1$ এর মতো চিন্তা করো।
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: Some problems to solve
Actually (n,1-n) is the solution of the problem 3..
In the divisional math Olympiad it was asked to find out the value of x-y=?
so the answer will be 2n-1
In the divisional math Olympiad it was asked to find out the value of x-y=?
so the answer will be 2n-1