MathDB
2023 MOAA Speed P7

Source:

October 13, 2023
MOAA 2023

Problem Statement

Andy flips a strange coin for which the probability of flipping heads is 12k+1\frac{1}{2^k+1}, where kk is the number of heads that appeared previously. If Andy flips the coin repeatedly until he gets heads 10 times, what is the expected number of total flips he performs?
Proposed by Harry Kim