[bmohlenhoff]

5400 = 90 min * 60 seconds

The test is a list of 23 true/false questions, so you can think of each question as a bit.

You've prearranged a list of 5400 unique 23-bit vectors, so he determines the bit vector with the most correct answers (ie. smallest Hamming distance) and leaves at whatever time offset corresponds to that bit pattern.

It's not a perfect scheme since you only have 5400 possible bit vectors, and 2^23 > 5400.