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Suppose I locked my ''very expensive'' mobile by a security code and now I forget the code. ;-( The things I remember about the code are:

$1)$ It consists a sequence of FOUR numbers, each from 1 to 60.

$2)$ All the numbers of the sequence are different.

$3)$ The 2nd number is twice the 3rd one.

$4)$ The 3rd one is prime.

How many different codes are possible having the above information?

My attempt: Since there are 10 primes between 1 to 60 twice of which is still inside 1 to 60, Hence 2nd and 3rd place can be filled with these 10 numbers, Now for the first place we have to choose from 58 numbers and for the fourth place we can choose from 57 numbers, Hence total possible codes are $10.57.58$? Am I right?

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Yes, you are right, and your reasoning is sound.

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  • $\begingroup$ Yes...you're correct on this! +1 $\endgroup$
    – amWhy
    Apr 21, 2013 at 3:36

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