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![[Post New]](/templates/default/images/icon_minipost_new.gif) 27 May 2008 14:28:00 IST
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Ok I ve deleted my solution. I did not know it was an RMO problem (my friend asked me this question) . What is this CBSE RMO? I know about the maths Olympiad conducted by Homi Bhabha centre.
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27 May 2008 14:43:05 IST
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ok...
a+13b= 11m
a+11b= 13n
solving thses two we have (a+b) =(156m- 110n)/2
happens at m=n=1.....
(a+b)=23.......
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"Logic is the systematic way of reaching the wrong conclusion with confidence" lol..... |
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27 May 2008 14:49:58 IST
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yeah dude dats the way i calculated the answer as 23 before......but it is incorrect, as the author said???
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"If you want to achieve something, the whole Universe conspires in your favour."
----The Alchemist
"He who joyfully marches to music rank and file, has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would surely suffice. This disgrace to civilization should be done away with at once. Heroism at command, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be a part of so base an action. It is my conviction that killing under the cloak of war is nothing but an act of murder."
"Not everything that counts can be counted, and not everything that can be counted counts."
"I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones."
"If A is a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut."
---Albert Einstein
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27 May 2008 15:01:14 IST
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a and b have to be positive integers. if u put m=n=1 , a and b will not be positive.
The answer given by oneyeartogo( now deleted) is also not perfect. you have only proved that a+b>= 28. it has not been proved that the value 28 can be achieved. In olympiads , such things matter a lot .
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27 May 2008 15:03:46 IST
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if a+b>=28.....then obviously min value of a+b will be 28.....
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"If you want to achieve something, the whole Universe conspires in your favour."
----The Alchemist
"He who joyfully marches to music rank and file, has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would surely suffice. This disgrace to civilization should be done away with at once. Heroism at command, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be a part of so base an action. It is my conviction that killing under the cloak of war is nothing but an act of murder."
"Not everything that counts can be counted, and not everything that can be counted counts."
"I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones."
"If A is a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut."
---Albert Einstein
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27 May 2008 15:06:49 IST
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Not necessary . the minimum value of a+b might be more than 28 . u may still be able to prove that a+b>=28
e.g. It can be proved that a+b >=2 ( because both a and b are positive integers.)
Does that mean that the value 2 can be achieved?
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27 May 2008 15:11:13 IST
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but we had to find the min value of a + b.....so if he had proved a+b>=28, so isn't the job done??
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"If you want to achieve something, the whole Universe conspires in your favour."
----The Alchemist
"He who joyfully marches to music rank and file, has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would surely suffice. This disgrace to civilization should be done away with at once. Heroism at command, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be a part of so base an action. It is my conviction that killing under the cloak of war is nothing but an act of murder."
"Not everything that counts can be counted, and not everything that can be counted counts."
"I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones."
"If A is a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut."
---Albert Einstein
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27 May 2008 15:12:51 IST
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I've proved that a+b>=2 . So is'nt the job done?
u have to prove that the it is possible to achieve the value 28 for some permissible values of a and b.
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27 May 2008 15:14:46 IST
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Is the answer 101? I am solving this for the first time.
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MAKING A MISTAKE IS HUMAN BUT REPEATING IT IS IDIOTIC. |
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27 May 2008 15:32:21 IST
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OK.......i got where i messed up this problem.......was gonna post the soln. but whooom.the power goes off........
look as rightly said....in the statement of the problem a and b are positive integers.........
so
a+13b= 11m
a+11b= 13n
solving thses two we have (a+b) =(156m- 110n)/2
this is not satisfied at m and n=1..........
we actually get b= (11m-13n)/2.....
and a= (169n-110 m)/2.........
so for a,b>0
we need 121/169<m/n < 11/13
and m and n are supposed to be both integers.........so we have m and n as 6 and 8 to satisfy the above inequality....
putting m=6 and n=8...
we have a+b= 56/2 = 28........
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"Logic is the systematic way of reaching the wrong conclusion with confidence" lol..... |
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27 May 2008 16:14:19 IST
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@ pramod - you've messed up again.
I don't understand how you get m=6 and n =8
Going by your calculation , we will get
a= ( 169 n - 121m) / 2
which gives a = 313 and b= -19
You got a+b= 28 because your value of (a+b) is wrong.
(a+b) = (156n -110m)/2
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27 May 2008 16:16:58 IST
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lol....everybody knows the answer....yet...no neat solutions...!!
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............tseb eht ma i |
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27 May 2008 16:58:32 IST
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According to the problem:
a+11b=13c
a+13b=11d
Solving these 2 equations we get
b=(11d-13c)/2
Since a,b are positive integers 11d-13c should be an even number
a+11b can take a minimum value of 13
a+13b can take a minimum value of 33(It cannot tke 22 because b will be in fractions)
The value of b decreases by 1 as the value of c or d increases by 1
The value of b should be such that a also becomes positive.
0<=b<=10
Therefore the least value that b can take such that a is also positive is 5.
Therefore by substituting b
a+11*5=78
a=78-55=23
Therefore the least value that a+b can take is 28.
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27 May 2008 17:02:57 IST
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I think the ans is 46.
a+13b=11m and a+11b=13n
Thus,b=11m/2-13n/2 and a=169n/2-121m/2
Hence,a+b=156n/2-110m/2 where m>1 and n>0,m,n are +ve integers.
a+b is min iff n is min and m is max under the condition that a+b 2
This occurs at n=2 and m=2,and the ans is 46.
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