1 Assume that you need to break a digit lock of five digits

1 Assume that you need to break a digit lock of five digits. Further assume that it takes 3 seconds to attempt one trial. Determine the average time to break this lock using brute force.

2 Assume that a password consists of not more than 3 alphabets (a to z) [it might be one, two or three alphabets] and further assume that it takes 2 seconds to attempt one combination. Determine the average time to break this password using brute force.

Solution

1) There are five digits, each digits has 10 possibilities, so the total possibilities are 10^5. The lock can be broken in 1st try ot 10^5 try and each has an equal change of occuring.

So the average time is 3(1+2+3...10^5)/10^5, which is 3*(10^5)/2 = 15*10^4