THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
70 Falmouth Street Portland, Maine 04103
43.6667° N 70.2667° W
Altitude: 10 feet below sea level
Founded January 1970
Julian Date: 245887.16
Julian Date: 245887.16
"Logic is the beginning of wisdom, not the end."
-Mr Spock
THE DAILY ASTRONOMER
Friday, February 7, 2020
Quiz XXI: A Logical Choice
First of all, no worries!
Logic is a tricky matter for most of us. We know of those highly complex logic problems in which you're trying to decide which man took which woman to which movie on which date and which snacks they purchased for what price and in which seat they sat and for how long and what rating did they give the movie on a scale of 1 - 10.
We also know the thickets and quagmires of mathematical logic that give us such artworks as the following:
Logic both hurts the brain and can bruise the spirit. That's why we're prefacing this quiz with "No worries." Everytime logic trips us up, our brain forges new neural pathways. All the same, we hope you enjoy the quiz: questions taken from Mind Trap and other mind bending games
1. Kasparov and Bobby Fischer played chess. They played seven games, each won the same number of games, and there weren't any draws or stalemates. How could this have happened?
2. In the tropics, if you drop a ball weighing five pounds from a height of 60 inches, will it fall more rapidly through water at 20 degrees Fahrenheit or water at 40 degrees Fahrenheit. Or will it make no difference?
3. A tallow obtained by burning ten candles will yield one extra candle. If you burned 1000 candles, how many extra candles could you make?
4. Susan said, "the day before yesterday my daughter was nine years old. Next year she will be twelve." Is her math wrong, or is this possible?
5. Why did the Treasury official tell the students that 1990 American dollar bills are actually worth more than 1989 American dollar bills?
6. You have seven identical coins. Six are the same in weight, but one weighs slightly less. Using a balance scale, how can you identify the one lighter coin?
7. Frank worked (once worked) for a packaging company. One day, Frank received four separate orders and mixed up the addresses. With nothing else for it, he applied the address labels at random. What is the probability that he addressed exactly three packages correctly?
8. One of the most famous of all logic problems: you encounter two robots. One always speaks the truth and one always lies. You don't know which is which. Next to them are two buttons: red and blue. If pressed, one of the buttons will kill you and the other would give you your greatest wish. The robots both know which button is which. In order to identify the buttons, you are allowed to ask one robot one question. Which question would you ask to which robot?
9. You are at the shore of a river with a boat. On the shore with you is a fox, a chicken and a head of lettuce. You have to transport them to the next shore. In your absence you know that the fox would eat the chicken. Also, in your absence, the chicken would eat the lettuce. You can only take one of them with you at a time. How do you transport the three of them safely across?
10. One room contains three light bulbs. An adjacent room contains three light switches, each of which controls one of the bulbs. None of the switches is labeled. How can you determine which switch controls which bulb by only being in the switch room once and then the bulb room once?
ANSWERS
1. Kasparov and Bobby Fischer weren't playing each other
2. 40 degrees Fahrenheit. At 20 degrees Fahrenheit the water would be ice.
3. 111
You get 100 candles from the original 1000, plus ten more from the tallow of the 100, plus one more from the tallow of ten.
4. It is possible. Susan's daughter was born on December 31st. Susan was speaking on January 1st. The day before yesterday was December 30th, when her daughter was nine. On December 31st, she turned ten. Later the same year (on December 31st) when Susan was speaking, her daughter will turn 11. The following year, she will turn twelve.
5. Because 1990 American dollar bills = $1,990, whereas 1989 American dollar bills equals $1,989.
6. Step 1: Separate the coins into two stacks of three, leaving one coin out. Place each stack on either side of the balance scale. If the scales balance, the coin left out is the lighter coin. If the scales don't balance, set the heavier stack aside.
Step 2: Place one coin from the lighter stack onto one balance and place one on the other. Place one coin aside. If the scale is balanced, the coin set aside is the lighter coin. If the scales are not balanced, the coin raised higher than the other is the lighter coin.
7. Zero! If three packages were labeled correctly, the fourth one would have had to have been labeled correctly, as well.
8. You should ask either robot, "If I asked the other robot what button I should press to get my greatest wish, what would it say?"
Let's say the red button would kill you and the blue button would give you your greatest wish.
The truth telling robot would say, "He would tell you to press the red button," because it always tells the truth and it knows that the other robot always lies. The lying robot would say, "He would tell you to press the red button," because it always lies and it knows the other robot always tells the truth. So, if you ask either robot, you would elicit the same answer. You would just press the other button, in this case the blue one.
9. First, take the chicken across the river first. Place it on the opposite shore. Row back and take the fox with you to the opposite shore. Bring the chicken back with you to the first shore. Leave the chicken on the first shore and bring the lettuce over to the opposite shore. Finally, row back to the first shore and bring the chicken back to the opposite shore.
10. Turn on one switch for about 30 minutes, during which time you remain in the switch room. Then, after 30 minutes, turn off the switch you had on and then turn on another. Immediately go into the bulb room. The light bulb that is on is controlled by the second switch you flipped. The bulb that is off but warm is controlled by the first switch you flipped. The bulb that is off and cool is controlled by the switch you never turned on.
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