What are the odds of guessing a number between 1 and 20 digits long?

A previous employee had set a password on our colour copier software, I
was told there was no over ride and we would have to reinstall the
software on the printer and would be charged £300 for an engineer to
do so. I said I'd rather have a go at guessing, and was told I could be
there for days as the password uses digits 0-9 and can be up to 20
digits in length. So I set off trying different numbers, some using
patterns (eg. the corners of the number pad etc), others just random,
after about 10 minutes and probably around 100 attempts, trying mainly
4 or 6 digit passwords, I guessed the correct password, 999. What are
the chances?

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