Brain Teasers & Puzzles
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On a geography test you have to tell which of two German cities is greater in population for all possible pairs of the 80 largest cities of Germany. (And that’s the only task on the test since it’s already 5 pages long.) But you didn’t study last night, and only even recognise half the cities, and don’t even know how those are ordered relative to each other. Your friend on the other hand studied dutifully all night and recognises all the cities and even knows how two cities are ranked relative to each other 60% of the time.
A week later you get the test-result and you have a higher score than your friend. How come?
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A confused bank teller transposed the dollars and cents when he cashed a cheque for Ms Denial, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Denial noticed that she had left exactly three times as much as the original cheque. What was the amount of the cheque ?
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Just do it, do not cheat! Because of you did, this test would be no fun. We promise that there are no tricks to this test.
Read the sentence below:
FINISHED FILES ARE THE
RESULT OF YEARS OF SCIENTIFIC
STUDY COMBINED WITH THE
EXPERIENCE OF YEARSThe question is: How many times do you see the letter F in the sentence above? Count them only once! Do not go back and count them again!
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The overly feminist rulers of a country decide that there are too many baby boys being born. The rulers decide to enforce a new law concerning child birth on their overly prosperous subjects. Each family is permitted to have as many children as they want, provided that they only produce baby girls. Once a baby boy enters the family, the family is no longer permitted to have children. Assuming each law abiding family wants to have as many children as possible, what will happen to the ratio of boys to girls, and why?
the ratio of boys to girls will go up.
the ratio of boys to girls will stay the same.
the ratio of boys to girls will go down.
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Jacob, his daughter, and the evil Joju lived in a city. Jacob was in debt to Joju, and Joju had his eye on Jacob’s daughter. Joju made a proposition: he would place a black stone and a white stone in a bag, and Jacob’s daughter would pick one out in front of the People of city. If she drew the white stone, Joju would forgive Jacob’s debt. If she drew the black stone, Joju would marry Jacob’s daughter. Jacob had no choice but to agree. Jacob’s daughter has no reason to trust Joju, and believes that he will place two black stones in the bag. How can she get out of marrying Joju?
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What is the least number of links you can cut in a chain of 21 links to be able to give someone all possible number of links up to 21?
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A boat of mass M1 is floating in a lake of water. The volume of the lake is V. The water surface is initially at height h, as measured relative to the lake’s floor. There is an anchor of mass M2 sitting on the boat’s deck. A person standing on deck picks up the anchor and throws it overboard. The anchor then sinks to the bottom of the lake, and the water surface height becomes h’.
Which of the following qualitative relationships is correct? What assumptions are you making about the values of M1, M2, h, and V?
h’ h
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Jacob and John are competing for the same girl. After years of battling, both decide to settle it by tossing a coin.
John produces a coin, but Jacob doesn’t happen to have one on him. Jacob is sure that the coin John has produced is loaded, i.e. it will come up with heads more than 50% of the time on average.
How do Jacob arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) Jacob and John are competing for the same girl, and decide to settle it with a coin toss. John has known the girl longer than Jacob have, so Jacob agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, Jacob only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
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You are a contestant on the Jacob game show. Three closed doors are shown before you. Behind one of these doors is a Bike; behind the other two are Goats. The contestant does not know where is the bike, but Jacob does.
The contestant picks a door and Jacob opens one of the remaining doors, one he knows doesn’t hide the bike. If the contestant has already chosen the correct door, Jacob is equally likely to open either of the two remaining doors.
After Jacob has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the bike if he stays with his first choice? What if he decides to switch?
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