You face three switches outside a room. Only one controls a bulb inside. You may enter the room once. How do you know which switch controls it?
Answer: Turn on switch one for a few minutes, turn it off, turn on switch two, then enter. If the bulb is on, it is switch two. If off but warm, switch one. If off and cold, switch three.
One door leads to safety and one to danger. One guard always lies, one always tells truth. What one question finds safety?
Answer: Ask either guard: Which door would the other guard say leads to safety? Then choose the opposite door.
Three people pay 30. Five is returned, two is kept as tip, and each person gets one back. Where is the missing dollar?
Answer: There is no missing dollar. They paid 27 total: 25 for the room and 2 tip.
Two ropes each burn in exactly one hour, unevenly. How do you measure 45 minutes?
Answer: Light rope A at both ends and rope B at one end. When A finishes, 30 minutes passed. Light B's other end; it finishes 15 minutes later.
Among 9 coins, one is heavier. Find it in two weighings.
Answer: Weigh 3 vs 3. If equal, the heavy coin is in the remaining 3. If not, it is in the heavier group. Weigh 1 vs 1 from that group.