Gordian Knot '16 - Fibonacci Sequence
A deck of 51 playing cards which consists of 3 aces is shuffled at random. The cards are then turned up one by one from top. Find the expected (average) number of cards to be turned up, until second ace appears.
Find more such problems at the math contest here: Gordian Knot - http://felicity.iiit.ac.in/