You face this classic puzzle in deductive reasoning:

A closed room contains a light bulb. Outside the room are four toggle switches, all initially off.
Exactly one switch controls the bulb.
You can flip switches however you want, but you’re allowed to enter the room only once to observe the bulb (its on/off state, and whether it’s warm).

Goal: Determine exactly which switch controls the bulb, using only one visit to the room.

Step-by-Step Strategy

You’re allowed to touch the bulb and check whether it’s on or warm. This allows you to gain more information than just sight.

Step 1: Create Four Unique States

To distinguish between 4 switches using a single bulb, we need 4 distinct observable states. We can achieve this by combining on/off with warm/cold.

Here is the exact procedure:

  1. Turn ON Switch 1 and Switch 2, and leave them on for about 10 minutes to let the bulb heat up.
  2. Turn OFF Switch 1. (Leave Switch 2 on).
  3. Turn ON Switch 3.
  4. Leave Switch 4 OFF.
  5. Immediately enter the room.

Step 2: Observe and Infer

Once inside, you touch the bulb and observe its state. There are exactly four possible outcomes, each uniquely identifying the correct switch:

  • Bulb is OFF and WARM → Controlled by Switch 1 (was on for 10 minutes, but turned off right before entering).
  • Bulb is ON and WARM → Controlled by Switch 2 (was on for 10 minutes, and left on).
  • Bulb is ON and COLD → Controlled by Switch 3 (was just turned on, so it hasn’t had time to heat up).
  • Bulb is OFF and COLD → Controlled by Switch 4 (was never turned on).

Final Answer

You only need to enter the room once.
By cleverly combining timing (to create warm/cold states) with switch combinations (on/off states), you can uniquely identify all 4 switches in a single visit!

Reference