MathDB
2019 C/CS6: Lightbulbs in a Circle

Source:

January 27, 2019
2019combinatorics

Problem Statement

There are 100100 lightbulbs B1,…,B100B_1,\ldots, B_{100} spaced evenly around a circle in this order. Additionally, there are 100100 switches S1,…,S100S_1,\ldots, S_{100} such that for all 1≤i≤1001\leq i\leq 100, switch SiS_i toggles the states of lights Bi−1B_{i-1} and Bi+1B_{i+1} (where here B101=B1B_{101} = B_1). Suppose David chooses whether to flick each switch with probability 12\tfrac12. What is the expected number of lightbulbs which are on at the end of this process given that not all lightbulbs are off?
Back to ProblemsView on AoPS