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A British spy is trying to escapre from the prison cell.

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A British spy is trying to escapre from the prison cell. [#permalink] New post 24 Oct 2009, 21:54
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A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.

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Re: Combinatorics [#permalink] New post 24 Oct 2009, 22:14
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rlevochkin wrote:
A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.


9C1(numbers)*6C2(buttons)*3sec(time)=9*15*3=405sec

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Re: Combinatorics [#permalink] New post 24 Oct 2009, 22:47
rlevochkin wrote:
A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.


= 9c1 x 2 (6c2) x 3 sec, or, = 9c1 x (6x5) x 3 sec ..... order matters.
= 9 x 2 (15) x 3 sec
= 810 second

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Re: Combinatorics [#permalink] New post 24 Oct 2009, 22:56
The order does not matter because the buttons are pressed simultaneously vs. one at a time

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Re: Combinatorics [#permalink] New post 24 Oct 2009, 22:59
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GMAT TIGER do you mean the order he pushes the two buttons matter?

Maybe I didn't understand the stem correctly but ".. push a pair of colored buttons simultaneously". Doesn't that mean that the order doesn't matter? He pushes two at a time, simultaneously. I got it like there are no button 1 and 2.

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Re: Combinatorics [#permalink] New post 24 Oct 2009, 23:09
Bunuel wrote:
GMAT TIGER do you mean the order he pushes the two buttons matter?

Maybe I didn't understand the stem correctly but ".. push a pair of colored buttons simultaneously". Doesn't that mean that the order doesn't matter? He pushes two at a time, simultaneously. I got it like there are no button 1 and 2.


Probably I did not understand the question on the pair of colored buttons.

I assumed that if it is a code, then probably how you press the colored buttons "red and black" matters. If these colored buttons are seperately placed, then still it matters. If the two buttons are placed simulteneously and can be pressed at a time, then the order doesnot matter.

However it seems the order doesnot mattter per the originator's post.

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Re: Combinatorics [#permalink] New post 25 Oct 2009, 00:34
I get 405sec going by bunnel's method..
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Re: Combinatorics [#permalink] New post 02 Nov 2009, 12:47
I got 405s, but I'm pretty certain that the spy is boned.
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Re: Combinatorics [#permalink] New post 02 Nov 2009, 13:38
Second thought-
Should we start counting the time from t+3 instead of t.
you need to count the time between the attempts and not the attempts itself -
i.e 1 st attempt 0 secs
2 nd attempt 3 secs
9C1*6C2 attempt (9C1*6C2 -1)*3 = 402 seconds.

The question says "He can make 1 attempt every 3 seconds" which could mean he needs to wait 3 seconds before making the first attempt (Kinda dumb IMO).

Anyhow I won't be surprised if the answer is 405 but for similar questions I would watch what is asked for very closely to rule out the possibility of a 402.

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Re: Permutation and Combination [#permalink] New post 28 Jul 2011, 11:30
Sudhanshuacharya wrote:
A British spy is trying to escape from his prison cell. The lock requires him to enter
one number, from 1-9, and then push a pair of colored buttons simultaneously. He
can make one attempt every 3 seconds. If there are 6 colored buttons, what is the
longest possible time it could take the spy to escape from the prison cell?


9 x 15 (there are 135 combinations) x 3 (one attempt per 3 seconds) = 405 seconds
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Re: Permutation and Combination [#permalink] New post 28 Jul 2011, 11:46
katealpha wrote:
Sudhanshuacharya wrote:
A British spy is trying to escape from his prison cell. The lock requires him to enter
one number, from 1-9, and then push a pair of colored buttons simultaneously. He
can make one attempt every 3 seconds. If there are 6 colored buttons, what is the
longest possible time it could take the spy to escape from the prison cell?


9 x 15 (there are 135 combinations) x 3 (one attempt per 3 seconds) = 405 seconds


I guess you arrived at 15 by doing 6C2.
So if there are 6 different colors then: is 4, greeen, red combination same as 4, red, green???
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Re: Permutation and Combination [#permalink] New post 28 Jul 2011, 11:52
Sudhanshuacharya wrote:
katealpha wrote:
Sudhanshuacharya wrote:

So if there are 6 different colors then: is 4, greeen, red combination same as 4, red, green???


Could you pls explain this, sounds interesting..
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Re: Permutation and Combination [#permalink] New post 28 Jul 2011, 12:03
So if there are 6 different colors then: is 4, greeen, red combination same as 4, red, green???[/quote][/quote][/quote]

Could you pls explain this, sounds interesting..[/quote]

Since he pushes the buttons SIMULTANEOUSLY #4 green, red combination is exactly the same as #4 red green
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Re: Permutation and Combination [#permalink] New post 28 Jul 2011, 12:11
katealpha wrote:
Since he pushes the buttons SIMULTANEOUSLY #4 green, red combination is exactly the same as #4 red green


Yes, it shud be the same.. when I solved the problem I too picked 6C2 subconsciously and came up with 405 .. but yes, to your point.. when you use a combination the order doesnt matter..
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Re: Permutation and Combination [#permalink] New post 14 Aug 2011, 13:40
6C2 * 9 * 3 = 15 * 9 * 3 = 405 seconds
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Re: Permutation and Combination [#permalink] New post 14 Aug 2011, 18:36
6 colors - total possible pairs = 6c2 = 15

1-9 - total possible options = 9

every attempt takes 3 seconds.

Total possible combinations = 15*9*3 = 405 seconds.
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Re: Permutation and Combination [#permalink] New post 18 Jan 2012, 11:13
Once you find 405 seconds, shouldn't you subtract 3 seconds from that answer because the 1st try doesn't require a three second wait while the other ones do. Essentially, only 134 tries require a 3 second wait, and thus shouldn't the answer be 402 seconds (134x3)?

Please let me know where I may be understanding the question differently.
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Re: Permutation and Combination [#permalink] New post 19 Jan 2012, 00:05
workingonit121 wrote:
Once you find 405 seconds, shouldn't you subtract 3 seconds from that answer because the 1st try doesn't require a three second wait while the other ones do. Essentially, only 134 tries require a 3 second wait, and thus shouldn't the answer be 402 seconds (134x3)?

Please let me know where I may be understanding the question differently.


I don't know where the question is from, and I wouldn't be at all surprised if 405 was the answer the question designer considers to be correct, but I agree with you. 405 is the number of possible codes, but 402 seconds is, by my interpretation of the question, the length of time required to test them, which is what the question asks for. That said, the wording isn't all that clear - can the spy test the first code immediately, or does it take 3 seconds to try the first code? Hard to say, and not really worth worrying about anyway since any real GMAT question will be precise about these types of points.

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Re: Permutation and Combination   [#permalink] 19 Jan 2012, 00:05
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