Question 1138065
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<pre>
When you use the words, consisting of three letters A,B and C (uppercase) of the length "n"  (n symbols), 


then the number of all possible codes is {{{3^n}}}.


In order for the probability to guess a password randomly be less  than 0.001, you need to have more than 1000 such codes (passwords).


It gives you inequality


    {{{3^n}}}  > 1000.


Its solution is


     n*log(3) > log(1000) = 3,   or


     n > {{{3/log((3))}}} = 6.28.


Since n must be integer, it gives you inequality n >= 7 as your <U>ANSWER</U>.
</pre>

Solved, explained and completed.