FYS: Puzzles and Paradoxes--Problem Set 8

Complete exactly three of the following five problems.

1. A family of two adults and three children, after having made it across the river, come to a gorge spanned by a rickety rope bridge. Since it is dark they will have to light their one and only torch with their one and only match (their one and only means of lighting the torch) to make sure they do not miss their footing. The father can make it across the bridge in 2 minutes; the mother in 3 minutes; the oldest child in 6 minutes; and the two youngest in 8 minutes each. Unfortunately, (a) the bridge can only hold at most two people at a time and the two must stay together, (b) the torch will go out after 26 minutes, and (c) no one can cross the bridge in the dark.

Is it possible for the family to get across the bridge before the torch runs out? Justify your answer.

2. You have a beat up 1989 Honda Civic abandoned with absolutely no gas in the tank in the middle of an empty parking lot. You also have a bucket of sand and a big stick of dynamite (and something to light the dynamite). Suppose you want to maximize the amount of damage to the car with the dynamite.

What arrangement of the sand and the dynamite will maximize the damage to the car? Justify your answer.

3. As you are diligently working on you logic homework, a devious and malevolent alien (oddly reminiscent of Marvin the Martian) freezes you, from the neck down, with his instantaneous stupefaction device, kidnaps you and puts you, still stupefied, in a strange room. The room has three buttons. The alien informs you that pushing button #1 triggers his disintegrator ray and kills you. Pushing button #2 unstupefies you and transports you back to Earth and freedom. Pushing button #3 triggers his instant vaporizer and kills you. The alien will let you make one and only one statement. If the statement is true, then the alien will choose which button he shall push. If the statement is false, then he will destroy you with his nefarious imploder gun.

Is there any statement you could make such that the alien must push button #2? Justify your answer.

4. Mathilda, while speaking normal everyday English, utters the sentence, "I am here now".

Is it logically possible for Mathilda's sentence to be false? Justify your answer.

5.[Bonus Point Problem] A worm is at the end of a one kilometer long rubber rope. The worm crawls along the rope at a steady unchanging pace of one centimeter per second. But after the first second the rope stretches uniformly (like a rubber band) to two kilometers. After the next second the rope stretches to three kilometers, and so on.

Will the worm be able to reach the end of the rope in a finite number of seconds?

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