BdMO National 2013: Junior 6
You have $1, 2, 3, 4, 5, 6, 7, 8, 9$ kg weights in your home. You have only one piece of each of the weights. You also have a balance. If you put a weight on the left side of that balance, its weight becomes twice. Every time you choose three weights to put on the balance in such a manner that the balance remains in equilibrium. On every turn, the total weight the balance can carry gets reduced by $3$ kg. At the first time the balance may carry at most $20$ kg in total. In how many ways can you keep weights on balance?
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Re: BdMO National 2013: Junior 6
এইটার উত্তর mathematically কিভাবে বের করবো ?? গুনে গুনে না ।
"Education is the most powerful weapon which you can use to change the world"- Nelson Mandela
Re: BdMO National 2013: Junior 6
If you are looking for some hints,
*edited to add a missed out case. (thanks to Mahi)
Last edited by Labib on Sat Jan 11, 2014 10:53 pm, edited 1 time in total.
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Re: BdMO National 2013: Junior 6
The question allows $2(w_{L_1}+w_{L_2}) = w_R$ too. Did you count those?Labib wrote: According to the statement,
\[2w_L = w_{R_1} + w_{R_2}\]
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Re: BdMO National 2013: Junior 6
Missed out on those I guess.*Mahi* wrote:The question allows $2(w_{L_1}+w_{L_2}) = w_R$ too. Did you count those?Labib wrote: According to the statement,
\[2w_L = w_{R_1} + w_{R_2}\]
I'll fix it anyway.
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- atiab jobayer
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Re: BdMO National 2013: Junior 6
I'm not sure if I can make it sound any easier than this Atiab.
I'd leave it to someone else who could come up with an easier solution.
Meanwhile, I'd give you a heads up. Please do not use "Banglish" in the forum. (I believe it is prohibited)
If you wish to right bangla, please use Avro/some other software.
I'd leave it to someone else who could come up with an easier solution.
Meanwhile, I'd give you a heads up. Please do not use "Banglish" in the forum. (I believe it is prohibited)
If you wish to right bangla, please use Avro/some other software.
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
- atiab jobayer
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- asif e elahi
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Re: BdMO National 2013: Junior 6
I think the answer is 1.I solved it by brute force.
- Fatin Farhan
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Re: BdMO National 2013: Junior 6
আমারও ১ আসছিল। গুনে গুনে করসিলাম
"The box said 'Requires Windows XP or better'. So I installed L$$i$$nux...:p"