Insight · ★★★★☆ · ~7 min
Color Switches
Bulbs flip by a neighbor rule. Does the process always stop?
by MindYourPuzzle
N light bulbs, each red or blue, in a row. At each step, you must toggle the state of every red bulb and its immediate right neighbor (or only the red bulb if it's the last).
Prove that you can always reach the all-blue state, and find the minimum number of steps.
Hints