Greg's practical brain food

Solutions at bottom

Problems

Number one

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?

Number two

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

Number three

Four switches can be turned on or off. One is the lightswitch for the incandescent overhead light in the next room, which is initially off, but you don't know which. The other three switches do nothing. From the room with the switches in it, you can't see whether the light in the next room is turned on or off. You may flip the switches as often and as many times as you like, but once you enter the next room to check on the light, you must be able to say which switch controls the light without flipping the switches any further. (And you can't open the door without entering, either!) How can you determine which switch controls the light?

Number four

Three surgeons and a clumsy cook go camping in the remote wilderness. The clumsy cook stumbles over the campfire as he is serving the surgeons, injuring himself and dumping hot stew on the hands of the surgeons. The cook's injuries need surgical treatment. The surgeons' injuries are minor but open. It turns out they brought the equipment necessary for the cook's surgery with them, and they can use the campfire to sterilize the tools. But there are only two rubber gloves. Because of the different surgeons' skills, all three of the surgeons are needed to operate on the cook, in sequence. How can this be done without any of them being exposed to the blood of any of the others?

Solutions

Number one

Push the cork into the bottle and shake the coin out.

Number two

A square manhole cover can fall into the hole on the diagonal; a round manhole cover cannot be dropped into the hole.

Number three

Turn on switches 3 and 4 and wait fifteen minutes or so. Then turn switch 3 off, turn switch 2 on, and enter the room. If the bulb is dark and cool, switch 1 controls it. If the bulb is bright and cool, switch 2 controls it. If the bulb is dark and warm, switch 3 controls it. If the bulb is bright and warm, switch 4 controls it.

Number four

The first surgeon operates with the first glove (glove A) inside the second glove (glove B). The second surgeon operates using just glove B. The third surgeon operates using glove A, turned inside out, inside glove B.

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