Go to the attic, turn on Switches 1 and 2, wait a few minutes, then turn off Switch 2 before ascending to the attic.
If the bulb is on, you conclude that Switch 1 is the winner.
If the bulb is off, but warm, you conclude that Switch 2 is the winner.
If the bulb is off, but not warm, you conclude that Switch 3 is the winner.
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