BecauseIhave nothing better to do, here are my solution attempts: 1. At time 00:00, light both ends of the first rope, and one end of the second rope. The first rope will burn completely in 30:00-at this point the second rope will be halfway burned, so then light the other end of the second rope. The remaining 30:00 of burn time will be cut in half, so when the second rope is completely burnt, 45:00 have passed. 2. This is probably not the intended solution, but assuming the coin hasahigher melting point than the bottle (especially if the coin is metal and the bottle is plastic), then melt the bottle to free the intact coin.Iguess you could also use your rope-lighter to burn the cork (assuming it isn’t rubber)… Must beabetter solution without resorting to lame assumptions… 3. Createasingle pile of coins by taking1coin from the first bag,2coins from the second, etc. until 100 coins from last bag. That’s 5050 coins, so the expected weight is 5050 oz. Weigh the pile, and the number of hundredth-ounces excess is the bag with the gold. So if it was 5050.25 oz, then the 25th bag has the gold. 4. Tip the cylinder sideways (probablya45 degree angle), and see if the water line touches two “opposite corners” (eg. the bottom left and the top right). If both corners are touched, cylinder is exactly half full (since that line would represent half-volume). If the water does not touch either corner, it is less than half full. 5. One point-the geographic North Pole. You can’t walk south from the South Pole. 6. This is the most frustrating one (for me). Since it’saballpark, perhaps the numbers represent baseball records-I see 714 for Hank Aaron’s old career home run record, and 61 for Roger Maris’ old season home run record. If that’s right, then the other numbers are 3725 (maybe Ty Cobb’s old hit record?), 169 (seems too low to bea”season hits” record), and 823 (maybe career stolen bases?). If I’m right, then without Googling to confirm numbers, you’d need to beamajor baseball nerd to get this (lame), and even if that is the “answer”, doesn’t seem much ofa”riddle” or “cipher” at all (double lame). Not worth more of my time… 7. This one is awesome!Ithink the intended solution is that for the number of red-eyed monks in the group, that number of days pass. Then at midnight of the next night, all the red-eyed monks kill themselves. The reason is that if there’s only one red-eyed monk, he will see that everyone else has brown eyes, so he must be the red-eyed one, and will kill himself at the first midnight. If there are two red-eyed monks, they will notice that one other monk has red eyes, and so will assume that the tourist was talking about the other one. The next day, they are still both alive, so they will realize they themselves must also have red eyes (or else “the first case” would apply, and they would have killed themselves already). So on midnight of the second night, they both kill themselves. If there are three monks with red eyes, it will take two midnight deadlines to pass before they realize they have red eyes-this isagreat recursive scenario. (Although,Ithink it is even more dramatic if the tourist was lying, and NONE of them have red eyes. Then ALL the monks kill themselves that night!) 8. Another one where my solution is probably not “intended”, butIcan’t think of another way. Plant one tree at the North Pole, and another at the South Pole. Then plant the other5inaring around the equator. Straight lines drawn from the poles through the equator trees will be5rows of trees, and the equator line is the 6th.Ican’t think ofasolution onafinite, flat two-dimensional surface. 9. Bud is telling the truth, so Jim robbed the bank. 10. Assuming you had an infinite amount of time, turn over every coin and put them into alternating piles. That way (infinity)-20 coins become tails, and ((infinity)-20)/2=infinity. This one also seems very lame. But working out 1, 3, 4, and7made this worthwhile.