In a room there are three switches. In another room (which you can't see from where the switches are) there is a light bulb. You can only enter the light bulb room ONCE. How can you determine which switch controls the light bulb?
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The three switches
Hints
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- Key idea: Enough information to solve the problem.
- Procedure (3 steps): Turn off switch 1 and turn on switch 2.
- Key idea: Total combinations: 2 × 2 = 4 possible states.
Solution
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Answer: Use the residual heat of the light bulb as a third signal.
Procedure (3 steps):
- Turn on switch 1 and wait 10 minutes.
- Turn off switch 1 and turn on switch 2.
- Enter the room and look at the light bulb (and touch it carefully to see if it is hot).
Interpretation of results:
| Observed status | Temperature | Switch | Explanation |
|---|---|---|---|
| On | Hot | #2 | You just turned it on |
| Off | Hot | #1 | It was on for 10 min |
| Off | Cold | #3 | Never turned on |
Key idea:
- Electrical states: 2 (on/off)
- Thermal states: 2 (hot/cold)
- Total combinations: 2 × 2 = 4 possible states
- Switches: 3 (we need to distinguish 3)
- Enough information to solve the problem
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