1. Burn one rope from both ends and the other rope from one end, all at the same time. When rope 1 consumes entirely (30min), burn the other end of the second rope, remaining 15 min. 30+15 = 45
2. Push cork entirely inside the bottle, and remove coin.
3. Grab 1 coin from bag 1, 2 coins from bag 2… and so on until 100 coins from bag 100. Use the scale. The weight should be between 1050 and 1051. Decimal points resulting from = Weight - 1050, should indicate the bag of gold. Ex. Weight = 1050.27 means that bag 27 has the gold.
4. Not sure about this one. But since it’s an empty room I assume there are 90 degrees corners, so Place the glass with the open side on one of the walls, and the side touching the other wall on the corner. If the water level is above the point where the glass touches the wall, then it is more than halffull and so on.
5. North Pole… But not sure what happens to polarity reaching the poles. Can you still go south being in the south pole?… Seems the answer should be only 1.
6. To complicated… probably has to do with the Rangers history and records… not a baseball fan.
7. Monks with red eyes will kill themselves all in the same night depending on the number of monks with red eyes. Example: If there are 2 monks with red eyes, they will kill themselves in 2 days. If only one, then that day. If 10, then 10 days later. And so on.
8. Can’t figure it out in a 2D plane. Credit to the person who suggested a sphere; Planting one on each pole, and the rest equidistant at the equator, and viewing them as 5 parallels and the equator itself as the lines. However, they wouldn’t be exactly “Straight lines”.
9. Jim robbed the Bank. If he was telling the truth, Bud and Sams arguments being false contradict each other. So Bud tells the truth, Jim robbed the bank and Sam hates Bud.
10. Take 20 coins and flip them into a separate pile. Number of tails on each pile is the same. Example: If you by chance take all the 20 coins facing tails of the infinity pile, and you flip them, all will be heads on the new pile and on the infinity pile since you took them all.