Solution to the light switch puzzle:
Flip the first switch and leave it on for a minute, then switch it off.
Ignore the second switch.
Flip the third switch and leave it on.
Hoof your way, painfully gasping, up the many flights of stairs to your apartment.
Examine the lamp.
If the bulb is off, and warm, then the first switch controls the lamp.
If the bulb is off, and cold, then the second switch controls it.
If the bulb is on, do I have to tell you…?