puzzles

If you put a coin in an empty bottle and insert a cork into the neck of the bottle, how could you remove the coin without taking the cork out or breaking the bottle?

You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route. How can you send the object securely?

You've been sentenced to death in an obscure foreign country which has a strange law. Before the sentence is carried out, two papers -- one with "LIFE" written on it and one with "DEATH" written on it -- are folded up and placed in a hat. You are permitted to pick out one of the papers (without looking), and if you choose the one with "LIFE" written on it, you are set free. Otherwise, the death sentence is carried out. On this occasion, a mean-spirited acquaintenance of yours, bent on your demise, has substituted the paper with "LIFE" written on it with another one with "DEATH" written on it. This person gleefully informs you of what he has done and that you are doomed to die. You are not permitted to speak to anyone about this misdeed, nor will you have a chance to switch the papers or the hat yourself in time. How will you avoid certain death?

You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won't get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. What's the fastest way to make full-sized ice cubes?

Why is it better to have round manhole covers than square ones?

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