I bought an air purifier which has [off, low, medium, high] settings and a single button. If it is on, the first button press activates the lights and subsequent presses increment the level with off following high. If off, the first press turns activates the lights and increments the level. There is a 30 second cool down before lights turn off. (This is all real world accurate.)
Assuming I was pressing the button remotely and repeated button presses are instantaneous; what is the minimum time it would take me to get the level to a known state and what is the sequence I should follow?
The first thing I came up with is 2.5 minutes.