Question

Killer robots are trying to take over the world. They know the password to the doomsday weapon is 5 digits long and contains either 0 or 1, and either 2 or 3, and either 4 or 5, and either 6 or 7, and either 8 or 9. If the robots can enter 5 passwords per second, how long (in seconds) will it take them to go through all the possible passwords?

Answer 1

I will assume the "password" may start with a 0

So let's first of all choose the number of passwords
which would be C(2,1) x C(2,1) x C(2,1) x C(2,1) x C(2,1)
= 2^5 = 32

13578 would be in that choice, but not 31578

So we now have to "arrange" each of these 32 numbers
which would give us 32 x 5! = 3840

at a rate of 5 passwords per second it would take
3840/5 or 768 seconds to crack it

Answer 2

Killer robots are trying to take over the world. They know the password to the doomsday weapon is 5 digits long and contains either 0 or 1, and either 2 or 3, and either 4 or 5, and either 6 or 7, and either 8 or 9. If the robots can enter 5 passwords per second, how long (in seconds) will it take them to go through all the possible passwords?

Answer 3

There are 2 choices for the first digit, 2 choices for the second digit, 2 choices for the third digit, 2 choices for the fourth digit, and 2 choices for the fifth digit. Therefore, there are a total of 2^5 = 32 possible passwords.

If the robots can enter 5 passwords per second, it will take them 32/5 = 6.4 seconds to go through all the possible passwords. However, this assumes that they will enter the correct password last. In reality, they may enter the correct password earlier or later than that.