| 1. |
Tom was going to drive from Philadelphia to New York, and then from New York back to Philadelphia
again. He bet his best friend Steve that he could average a speed of 60mph for the entire round trip.
However, on the way to New York, he encountered heavy traffic and only average 30mph for the first half
of the trip. How fast must he drive on the way back to Philadelphia in order to win his bet?
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| 2. |
You are an anthropologist who is studying two South American tribes - the Bawi and Mawi. The Bawi
are known for always telling the truth, and the Mawi are known for always telling lies. Other than
that, the two tribes are indistinguishable. As you are walking through the rainforest, you encounter
two tribesmen, who appear to be from differing tribes. The only problem is you don’t know which is
which. Can you determine who is from which tribe by asking only one question?
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| 3. |
You have in your possession 9 coins identical in appearance, of which one is counterfeit and weighs
slightly more than the others. With a simple balance scale, how can you determine which is the
counterfeit in only 2 weighings?
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| 4. |
At McDonald's you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number
of nuggets that it is not possible to obtain by purchasing some combination of boxes?
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| 5. |
One morning, John the milkman came upon two ladies who asked him for two quarts of milk each. One
lady had a five-quart pail and the other had a four-quart pail. John had only two ten-gallon cans,
each full of milk. How did he measure out exactly two quarts of milk for each lady?
(There are 4 quarts in a gallon)
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| 6. |
There are one thousand lockers and one thousand students in the school. The principal asks the first
student to go to every locker and open it. Then he has the second student go to every second locker and
close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he
closes it. The fourth student does this to every fourth locker, and so on. After the process is
completed with the thousandth student, how many lockers are open?
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| 7. |
You are an FBI agent assigned to locate counterfeit money. On one particular raid, you encounter
five bags of coins. All of them look alike, but a tipster has told you that only one bag is
counterfeit, and in that bag, each coin weighs one gram less than the real coins should. If you have
a gram scale on hand, how can you determine which bag is counterfeit after only one weighing?
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| 8. |
Three men gather for lunch in the countryside. One man has brought 3 loaves of bread, while
another has brought 4 loaves. The third man has brought nothing, but claims that he will pay his
fair share with the 14 dollars in his pocket. The other two agree. They sit down to eat, and all
three consume equal amounts of the bread. After the meal however, they get into an argument over
the correct method to fairly divide up the third man’s 14 dollars. What is the most fair division?
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| 9. |
A mathematician wishes to create a balance scale that can weigh any object who weight in pounds
is a whole number. The object will be placed on one side of the scale, and various weights of known
weight will be placed on the other. What is the minimum number of weights needed to be able to weigh
any object 31 pounds or less?
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| 10. |
The mathematician from problem #9 is unsatisfied with his scale because he still feels
that it uses too many weights. What is the minimum numbers of weights needed if the conditions are
changed to allow weights to be placed on either side of the scale. (For example, a 5 pound weight and
a 3 pound weight can be used to weigh a 2 pound object if the 3 pound weight and the object are
placed opposite the 5 pound weight.)
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| 11. |
How many students must be in a classroom in order for the probability that at least two of them
share a birthday be greater than ½?
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| 12. |
Three men (A, B, and C) are to be involved in a three-way duel. As part of the rules of the duel, each man takes his
turn and fires one shot at whomever he likes. Then the turn passes to the next man (who is still alive), and he then
fires at whomever he likes. This continues until only one man remains. Gentleman A is to fire first, followed by
gentleman B, and finally gentlemen C fires last.
These three men also have differing skills at firing a gun. The probability that A hits and kills his target is
one-third, whereas the probability of C hitting and killing his target is one-half. B is an expert shot and is
guaranteed to kill whomever he fires at 100% of the time.
Where should gentleman A fire his first shot if he wants to maximize his chance of surviving this game?
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| 13. |
In the 1980’s, a television show was aired called Let’s Make a Deal. During part of the show, the
host would show a contestant three closed doors on stage. The contestant was told that behind two of
the doors was a goat and behind the remaining door was a new car, and that they would win whatever was
behind the door they chose. At this point, the contestant then randomly picked a door. Before the door
was opened, the host would open up a different door to reveal that there was a goat behind it. The
contestant was then given the option to either stick with their original door, or switch to the third
remaining door. Is it advantageous door the contestant to switch doors, to keep the original, or does
it not matter?
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| 14. |
As an anthropologist, you return again to South America to resume your study of the Bawi and Mawi
tribes (from question #3). However, your research has been complicated by the recent discovery of a
third tribe, the Zawi, who are known for answering truthfully and lying at random. While in the jungle,
if you were to come across one man from each tribe, how could you determine who was who by using only 3
yes or no questions. Each question can only be directed at one man. (Assume that each man knows the
identities of the other two).
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| 15. |
You have in your possession 12 coins identical in appearance, of which one is counterfeit and weighs
either more or less (you don’t know which) than the others. With a simple balance scale, how can you
determine which is the counterfeit in only 3 weighings?
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