Solution – one entry is enough

Why a single entry can work When you look at the bulb you can observe two independent properties: 1. Whether it is lit (on/off). 2. Its temperature (cold, warm, hot). If we arrange the four switches so that each produces a unique combination of these two properties, a single glance inside tells us exactly which switch controls the bulb.

Plan – give each switch a distinct “signature” before you go in

Switch	Action before entering	Bulb state when you enter
1	Turn on for ~5 min, then turn off	Off & hot
2	Turn on for ~2 min, then turn off	Off & warm
3	Leave on	On (bright)
4	Never touch (keep off)	Off & cold

Procedure

Flip switch 1 on, wait about five minutes, then turn it off.
Flip switch 2 on, wait about two minutes, then turn it off.
Flip switch 3 on and leave it on.
Do nothing with switch 4.

Now walk into the room once and feel the bulb:

Lit → switch 3 is the correct one.
Off & hot → switch 1 is correct.
Off & warm → switch 2 is correct.
Off & cold → switch 4 is correct.

Each possible observation is unique, so a single entry suffices. Therefore the minimum number of times you must enter the room is one.

195. Find Correct Switch

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