Wiring Switches to Light Bulbs

TL;DR

This paper investigates the minimal number of bulbs that can be lit in a system of n buttons and bulbs, where each button toggles its own bulb and up to two others, establishing a fundamental lower bound.

Contribution

It provides a sharp lower bound on the number of bulbs that can be lit regardless of button actions in a specific toggle system.

Findings

Established the minimal guaranteed number of lit bulbs in the toggle system.

Derived bounds applicable to systems with local toggle interactions.

Contributed to understanding the combinatorial limits of toggle-based systems.

Abstract

Given n buttons and n bulbs so that the ith button toggles the ith bulb and at most two other bulbs, we compute the sharp lower bound on the number of bulbs that can be lit regardless of the action of the buttons.