$22$ light bulbs are given. Each light bulb is connected to exactly one switch, but a switch can be connected to one or more light bulbs. Find the least number of switches we should have such that we can turn on whatever number of light bulbs.
Source: Kosovo Mathematical Olympiad 2022, Grade 11, Problem 1
Tags: combinatorics
$22$ light bulbs are given. Each light bulb is connected to exactly one switch, but a switch can be connected to one or more light bulbs. Find the least number of switches we should have such that we can turn on whatever number of light bulbs.