Solution to Locomotive Problem (Mosteller, Fifty Challenging Problems in Probability)
Solution 1:
Choosing $2\times 60 - 1$ gives an unbiased estimate of $N$.
Choosing $60$ gives a maximum likelihood estimate of $N$.
But these two types of estimator are often different, and indeed this example is the one used by Wikipedia to show that the bias of maximum-likelihood estimators can be substantial.