I appreciate the numerical theory in the answer, but I don't buy into that. A Monte Carlo run shows that 90 is the most likely value, though this decreases slowly. Picking 5 random values from a list, where N is the highest value in the original list, and 90 is the highest of the 5 observed values, and running for 1 million trials, I get a table that looks like this. (I've not listed all values to 190, the last N that had any hits.)
N *** % 90 4.63% 91 9.01% 92 13.13% 93 17.02% 94 20.74% 95 24.21% 96 27.53% 97 30.72% 98 33.71% 99 36.58% 100 39.30%
From this run, the chances are even that N is less than or more than 105.
How to reconcile this result with the numerical analysis?
Also, if the numerical analysis has 2 valid answers, then there must be a range of valid answers in that region. It seems to me that this problem doesn't have an answer, but a handwaving "something about here" result.