The Solution: This is a classic puzzle that requires using more than just sight.

1. Turn on Switch 1. Leave it on for about 5-10 minutes. This will warm up the light bulb.
2. Turn off Switch 1. Immediately turn on Switch 2.
3. Leave Switch 3 in the "off" position.
4. Now, open the door and go into the room.

You will observe three possibilities:

• If the light is ON: The switch that controls it is Switch 2. (This is the most obvious one).
• If the light is OFF but the bulb is WARM to the touch: The switch that controls it is Switch 1. (Because you left it on long enough to heat the bulb).
• If the light is OFF and the bulb is COLD to the touch: The switch that controls it is Switch 3. (Because it was never turned on).

This solution brilliantly uses the secondary property of a light bulb: heat.

The Solution: The key is to realize that you can't just make one trip. You need to set up supply depots along the way. The camel must eat bananas to go forward, but you also need to leave bananas at depots for the return trips.

The strategy involves multiple trips and "leaving" bananas at certain points.

1. First Leg (Mile 0 to Mile X):

   • You have 3000 bananas. The camel can carry 1000, so you'll need 3 trips (2 forward, 1 back) to move all bananas past point X.
   • For each mile, the camel makes 2 trips forward and 1 trip back, eating a total of 3 bananas per mile.
   • You want to reduce the number of bananas to 2000, because then you'll only need 2 trips for the next leg. To get from 3000 to 2000, you need to consume 1000 bananas.
   • So, 1000 bananas / 3 bananas per mile = 33 miles. Let's round this down to 333 miles.
   • At the 333-mile mark, you will have 3000 - (333 * 3) = 3000 - 999 = 2001 bananas. You leave 2000 here and take 1 back to the start. Now you are at the start with 0 bananas.

2. Second Leg (Mile 333 to Mile Y):

   • You pick up the 2000 bananas at the 333-mile mark. Now you only need 2 trips (1 forward, 1 back) to move them past point Y.
   • For each mile, the camel makes 1 trip forward and 1 trip back, eating a total of 2 bananas per mile.
   • You want to reduce the number of bananas to 1000. To get from 2000 to 1000, you need to consume 1000 bananas.
   • So, 1000 bananas / 2 bananas per mile = 500 miles.
   • So, you travel 500 miles from the 333-mile mark, which brings you to mile 833.
   • At the 833-mile mark, you will have 2000 - (500 * 2) = 1000 bananas. You leave them all here.

3. Final Leg (Mile 833 to Mile 1000):

   • You pick up the 1000 bananas at the 833-mile mark.
   • The remaining distance is 1000 - 833 = 167 miles.
   • The camel eats 1 banana per mile, so it will eat 167 bananas for the final trip.
   • You arrive at the market with 1000 - 167 = 833 bananas.

Final Answer: The maximum number of bananas the merchant can get to the market is 833.

The Solution: The man is a dwarf (or a very short person).

• In the morning, he can easily reach the button for the ground floor (G or 1) with his umbrella or by stretching.
• When he returns from work, he can only reach the button for the 7th floor. He can't reach the 10th, so he has to walk the rest of the way.

This puzzle plays on our assumption that the man is of average height.

The Solution: This is a classic deduction puzzle.

1. Go to the barrel labeled "Apples and Oranges". Since you know this label is wrong, it cannot contain a mix. It must contain only apples or only oranges.
2. Take out one fruit from this barrel.
   • If you take out an apple: This barrel must be the "Apples" barrel.
   • If you take out an orange: This barrel must be the "Oranges" barrel.
3. Now, look at the other two barrels.
   • One is labeled "Apples" and the other is labeled "Oranges".
   • You have now correctly identified one barrel (e.g., the one you just took the apple from is "Apples").
   • The barrel labeled "Oranges" cannot be "Oranges" (because you know the original "Apples and Oranges" barrel was the real "Oranges" one), and it cannot be "Apples" (because you just found the real "Apples" barrel). Therefore, it must be the "Apples and Oranges" barrel.
   • By elimination, the final barrel, labeled "Apples", must be the "Oranges" barrel.

Example Walkthrough:

• Barrel 1: Labeled "Apples" (Wrong)
• Barrel 2: Labeled "Oranges" (Wrong)
• Barrel 3: Labeled "Apples and Oranges" (Wrong)

1. Go to Barrel 3. Take out an apple.
2. So, Barrel 3 is the "Apples" barrel.
3. Now look at Barrel 1 (Labeled "Oranges"). It can't be "Oranges" (because Barrel 3 is Apples). It can't be "Apples and Oranges" (because Barrel 3 is the pure "Apples"). So, Barrel 1 must be "Apples and Oranges".
4. Finally, Barrel 2 (Labeled "Apples") must be the "Oranges" barrel.

The Solution: The murderer is the Business Partner.

The Logic: The clue "The key is in the timing" tells us to scrutinize the alibis for inconsistencies.

1. Let's assume the Business Partner is telling the truth. He was in a meeting with the victim until noon, then left.
2. If the Business Partner left at noon, the meeting must have ended at noon.
3. Now, let's look at the Personal Assistant's statement: "I left the office at 10 AM and didn't return until 3 PM."
4. If the Personal Assistant left at 10 AM, she would not have been in the office for the meeting that the Business Partner claims took place until noon.
5. This means the Business Partner's statement ("I was in a meeting with him until noon") is impossible if the Personal Assistant was gone. He couldn't have a meeting with the victim if the victim was alone in the office.
6. Since the Business Partner's story contains a logical impossibility based on the other person's alibi, he is the one lying. He fabricated the alibi to cover up the fact that he was the killer.

The wife and assistant's alibis don't contradict each other or create any logical paradoxes.