Take a chance with the padlock

Discrete Mathematics Level 3

You are a given a standard 4 digit padlock, where each digit can be {0, 1, ..., 9}.

You are told that you have 3 attempts to unlock the padlock. You only need to be correct in 1 of these 3 attempts to be successful.

What you are not told, however, is that any digit in the correct combination is at most 1 unit difference from all the other 3 digits.

What is the probability that you will succeed (to 3 significant figures)?

Note that you are not stupid. You will remember the unsuccessful attempts, and avoid them in future attempts.

Note that 0 and 9 can be considered to be a unit difference


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