Keyless Entry Math Puzzle

Diana was admiring the output of her new program to generate random numbers. She had printed out the first ten numbers of the results. She soon noticed something interesting. Each of the 10 numbers had exactly one digit, in the proper placement, of the 5 digit code she used to open her car door without a key.

In the first number 14073, for example, Diana's car code could not be 34170 (two digits correctly placed) or 92365 (none).

Find Diana's car entry code from these first 10 randomly generated numbers:

14073
79588
05892
84771
63136
42936
37145
50811
98174
29402

Adapted from a math puzzle by Mark Hollis.

Click to find the answer to this math puzzle.