## BdMO National 2013: Junior 6

BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### 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?

Kiriti
Posts: 27
Joined: Mon May 13, 2013 5:05 pm
Location: 401/1 South Paik Para, Kalyanpur, Mirpur, Dhaka-1216

### 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

Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm

### 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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*Mahi*
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### Re: BdMO National 2013: Junior 6

Labib wrote: According to the statement,
$2w_L = w_{R_1} + w_{R_2}$
The question allows $2(w_{L_1}+w_{L_2}) = w_R$ too. Did you count those?

Use $L^AT_EX$, It makes our work a lot easier!

Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm

### Re: BdMO National 2013: Junior 6

*Mahi* wrote:
Labib wrote: According to the statement,
$2w_L = w_{R_1} + w_{R_2}$
The question allows $2(w_{L_1}+w_{L_2}) = w_R$ too. Did you count those?
Missed out on those I guess.
I'll fix it anyway.
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

atiab jobayer
Posts: 23
Joined: Thu Dec 19, 2013 7:40 pm

### Re: BdMO National 2013: Junior 6

Vai Eku sohoj basai lekhen
math champion

Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm

### 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.
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

atiab jobayer
Posts: 23
Joined: Thu Dec 19, 2013 7:40 pm

### Re: BdMO National 2013: Junior 6

I want to know what is the final answer
math champion

asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: BdMO National 2013: Junior 6

I think the answer is 1.I solved it by brute force.

Fatin Farhan
Posts: 75
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"The box said 'Requires Windows XP or better'. So I installed L$$i$$nux...:p"