Probability
On their daily commute to Mars, 100 aliens sit in a passenger spaceship with 100 seats (labelled 1-100). Each alien has a ticket (1-100), and they enter the spaceship in the order of their ticket values. But alien with ticket number 1 can't read human numbers, and sits in a random seat. The following 98 aliens (n.s 2-99), will sit in their assigned seat if it is free, but with otherwise randomly choose a seat.
What is the chance that alien 100 will sit in seat 100?
Hint: start with smaller cases of 2,3, 4 or 5 aliens.
Number Theory
Given that x^(x^(x^(x^(x^(x^...))))) =2, what is x?