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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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!

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??

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)

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!