The situation stops being a problem when someone either chooses seat 1 or seat N. Because: - If at any point someone chooses seat 1, then everyone else will g

The situation stops being a problem when someone either chooses seat 1 or seat N. Because: - If at any point someone chooses seat 1, then everyone else will get their chosen seat. -If at any point someone chooses the last seat, everyone but the last guy gets his seat. The last guy gets seat 1, because it has to be free (if it wasn't , then my first condition would have applied). So only seat 1 and N are possible, both having equal chance, thus 50%. You can notice that the two conditions that resolved the "seat being taken" problem were when someone sat in a seat that no one else would have a ticket for. What kinds of seats are those? The 1st seat, the last seat, and empty seats. This means that by adding L-N empty seats, the chances of the last guy having his seat is 1/(L-N + 1st seat + last seat) = 1/(L-N+2)