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Combinatorics Question

by Elena89 » Tue Nov 15, 2011 3:51 am
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?
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by shankar.ashwin » Tue Nov 15, 2011 3:56 am
Refer https://www.beatthegmat.com/basic-combin ... 92274.html
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by neelgandham » Tue Nov 15, 2011 4:01 am
Longest possible time = He could open the door in the last attempt.

Total number of attempts = 9*(6!/(4!*2!))=9*15 =135
Time between attempts = 3
Number of intervals between attempts = 135-1 = 134
Total time taken =134*3 = 402 seconds

Correct me if I am wrong!
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by shikh » Tue Nov 15, 2011 7:53 am
choosing 2 color buttons from 6 = 6C2= 15
choosing 1 number from 9= 9C1=9
==> 15*9=135
attempt every 3 secs= 135*3=405
answer is 405
am i ryt??
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by fueledGMAT » Tue Nov 15, 2011 9:08 am
405 seconds

You first use the combination 6C2 = 15
Since there are 9 numbers to choose from, each permutation could be for the 15 possible color combinations, so 15x9 = 135

Since the spy can only use one of the 135 possible combinations every 3 seconds, the maximum amount of time is 135x3 = 405 seconds!

Great problem (took me 1min, 42 seconds to do the math)
"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery
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by fueledGMAT » Tue Nov 15, 2011 9:09 am
neelgandham wrote:Longest possible time = He could open the door in the last attempt.

Total number of attempts = 9*(6!/(4!*2!))=9*15 =135
Time between attempts = 3
Number of intervals between attempts = 135-1 = 134
Total time taken =134*3 = 402 seconds

Correct me if I am wrong!
Bah I forgot about the time reference and intervals, you were correct to subtract 1... good show!
"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery
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