MathDB
2022 Combo Div 1 P4 (Div 2 P8)

Source:

February 28, 2022
combinatorics

Problem Statement

The CMU Kiltie Band is attempting to crash a helicopter via grappling hook. The helicopter starts parallel (angle 00 degrees) to the ground. Each time the band members pull the hook, they tilt the helicopter forward by either xx or x+1x+1 degrees, with equal probability, if the helicopter is currently at an angle xx degrees with the ground. Causing the helicopter to tilt to 9090 degrees or beyond will crash the helicopter. Find the expected number of times the band must pull the hook in order to crash the helicopter.
Proposed by Justin Hsieh