- Introduction
- Questions List
- Question 6: Just Do Not Cancel Anything
- Question 26: The Cat With the Magical Powers
- Question 41: A Wanderer, Two Questions and Three Ghosts
- Question 45: How Do the Smurfs Save Their Lives
- Question 90: Around the World
- Question 92: Duel By 50 Coins
- Question 94: Glasses In the Hardness Test
- Question 100: Handshakes
- Answer
- References
Introduction
“Kommen drei Logiker in eine Bar” was written by Holger Dambeck in German. The book includes 100 interesting questions about mathematics, logistics and geometry. I list some difficult questions below.
《三个逻辑学家去酒吧》是由霍格尔•丹贝克（德国数学家、逻辑学家，《明镜周刊》在线版科学与健康栏目主编）所写、由罗松洁翻译的书。 书中包含了100道有趣的关于数学、逻辑、几何的谜题。需要充分发挥创造力、想象力和空间能力去解决。 以下列出一些颇有难度、也很有意思的问题。 （如果想看中文题目，请购买此书中文版。）
Questions List
Question 6: Just Do Not Cancel Anything
There are two fuses with different lengths and these two fuses can be burned for exact one minute. Based on that, can you measure a duration of 45 seconds and how?
Second question: there are only one fuse that can be burned for exact one minute. Can you measure a duration of 10 seconds and how?
Rules: you cannot use rulers or fold the fuse.
Question 26: The Cat With the Magical Powers
A crazy and magical cat wants to run from PlaceA to PlaceB. The entire distance is 1800 km.
This cat is incredibly fast and likes to accelerate.
A rope with a metal can is tied at the cat’s tail. Every time the cat jumps, the can behind it will slam on the ground and make a sound. When the cat hears the sound, it will instantly double its speed.
Every jump of the cat is exactly 1 meter long and this length will not change no matter how fast it runs.
This cat departs with a speed of 15 km/h from PlaceA at 9:00. WHen can it arrive PlaceB?
Rules: ignore the fact that the speed is doubled instantly without any delay and other physical laws apply to this cat.
Question 41: A Wanderer, Two Questions and Three Ghosts
When the person answering the questions either only lies or only tells the truth, it is difficult to ask two persons the right questions to get the right answer. Now the question is more complicated: not only lying ghosts and honest ghosts, but also ghosts that sometimes lie and sometimes tell the truth.
A hiker was on the way to find a hotel. When he arrived in a three-way intersection, it was already dark. There were three ghosts standing there, and each ghost has its own different manifestations of truth. The ghost of day only tells the truth, the ghost of night only tells lies, and the ghost of dusk sometimes tells the truth and sometimes tells lies according to its moods.
These three ghosts all look the same that we cannot distinguish them or tell the difference. The hiker can ask only two questions in total. He can ask the same ghost or two different ghosts.
So, what questions and whom should he ask to find the right path?
Hint:
If there are only two types of ghosts, telling truth or lying, it is simple and one question is enough. Just ask a question to make sure both of the ghosts will give the same answer. For example, the question is: the ghost who are different from your type will tell me which the right path is. Both types of ghosts will give the wrong direction and then just take the other one that will be the correct one.
However, in this case, the third type of ghost makes the situation more complicated. But the hiker can ask two questions. So he can use at least one question to solve this uncertainty.
The strategy is using the first answer to determine which ghost to be asked the second question.
In any case, it is important that the hiker use the first question to ensure that he will never ask the second question to the ghost of dusk, because its awkward answer is almost impossible to help him. The key is to use the first question to identify one or even two ghosts that are not ghosts of dusk.
Question 45: How Do the Smurfs Save Their Lives
Gargamel (格格巫) caught 100 Smurfs (蓝精灵). Each Smurf was held in a separate small room and they cannot communicate with each other. On the first day, Gargamel brought all 100 imprisoned Smurfs into a hall with a chandelier hanging from the ceiling.
“No one can escape from this cell,” he said, “But I can give you a chance to regain your freedom. From tomorrow, I will randomly choose one of you every day and bring him from his room to this hall. The selected Smurf can turned on or off the light. He can choose what do do and the light can be switched only once. Or he can also choose to do nothing. This is up to him. Then I will bring him back to his room.”
These imprisoned Smurfs were full of doubts. What did Gargamel want to do?
The wizard continued: “One day, one of you was brought to this hall and knew that all the other Smurfs had been in this room at least once. Then he should come and tell me. If he was right, all of you would be released. If he was wrong, all of you must die!”
Now these Smurfs were even more confused. What should we do?
“You can still stay together in this hall for a while and discuss it,” Gargamel said. “I have already turned on the light in this hall and let it keep being on. When you are brought back to your own rooms again in an hour, it will also continue to light up. And you will never see each other again!”
Fortunately, these Smurfs are smarter than Gargamel. They came up with a strategy and gained freedom. What is the strategy?
Question 90: Around the World
There is an aircraft team on a small island. All airplanes are of the same model and fly at the same speed. Every time the oil is filled, one airplane can fly half a circle around the earth.
Fortunately, every airplane can refuel at any time in the air. Fuel is sufficient, but is supplied only on the island.
How many airplane are required to get an airplane to fly around the earth and all airplane must eventually fly back to the island safely?
Hint: in order to be convenient, we assume that refueling on the ground, refueling in the air, taking off, landing and turning around, all these actions can be done instantaneously without time consumption.
Question 92: Duel By 50 Coins
There are 50 coins in a row on the table. These coins have different values and we cannot move them.
In this game, you and your opponent take turns to take a coin from the left or right end of the row of coins. Each of you can re-determine from which end of the side to take a coin when it is your turn to take. You take first.
The purpose of this game is to get as much money as possible or more than your opponent. Note that the values of these coins are different.
Please give a strategy that you can always get at least as much money as your opponent at the end of the game.
Hint: if you are looking for a strategy to take as much as possible, it will make this game too difficult. You can also win with a small advantage. When you have to, you can also get exactly the same as your opponent. Please do not look for the best strategy, but to find a simple strategy that is possible and successful. This strategy works well in all situation where coins are distributed randomly. Be as generic as possible.
Question 94: Glasses In the Hardness Test
There is a factory that produces glasses that are particularly difficult to break. These glasses survive from the impact on concrete, even if they fall from many storeys high. The hardness of the glasses every day is unstable depending on many conditions such as the addition or the temperature. But the quality of all the glasses produced in one day is always the same.
Every evening, the quality inspector takes one glass from the daily product and lets it fall from a higher and higher floors in the testing tower until it breaks. The testing tower has ten floors. So in the worst case, the quality inspector must drop the glass ten times until it is found that the highest floor for the glass.
However, running up and down for the testing makes the quality inspector exhausted. One night, he came up with an idea, and he tried to use two glasses to do the drop testing instead of one glass. If the first glass breaks, he can continue to test with the second one.
When the quality inspector used two glasses to do the testing, how many tests does he need to try at most?
Another more difficult question: if the testing tower has 101 floors, then how many tests?
Rules:
- The testing tower has a ground floor and there are ten floors above.
- We assume that as long as a glass is not broken during the testing, it does not have any damages or cracks. The glass will not break easily or faster in the next testing.
Question 100: Handshakes
A couple, Kai and Mirijana came to a party where they met other couples who are paired. The host came up with a special game to welcome everyone: everyone has to shake hands with all the people they do not know.
After a while, Kai made a survey and found out that the other nine people at present were shaking hands with different numbers of people.
How many people did Mirijana shake hand with?
Answer
If you want to find out the correct answers, send email to me or buy the book.
如果你想知道答案，发电邮给我或者买书吧！
References
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