Interesting math question: If three cats catch three mice in three minutes, how many cats will catch 100 mice in 100 minutes?

This is an old and interesting question, and the common answer is this: If three cats catch three mice in three minutes, they must catch 1 mouse in 1 minute. Therefore, if it takes 1 minute to catch 1 mouse, then the same three cats catch 100 mouse in 100 minute.

Unfortunately, the problem is not that simple. The answer just now actually uses certain assumptions, which are undoubtedly not mentioned in the title. This hypothesis holds that three cats focus all their attention on the same mouse, catch it within 1 minute through cooperation, and then turn their attention to another mouse together.

However, suppose three cats do the same thing. Every cat chases 1 mouse and catches them in 3 minutes. According to this idea, three cats still caught three mice in three minutes. So they caught 6 mice in 6 minutes, 9 mice in 9 minutes and 99 mice in 99 minutes. Now we are faced with a computational problem. How long will it take the same three cats to catch the100th mouse? If it still takes them three minutes to catch the mice, it will take the three cats 102 minutes to catch 102 mice. Catch 100 mice in 100 minutes-this is the efficiency index for cats to catch mice. We definitely need more than three cats and less than four cats, so the answer can only be four cats, although it is a bit wasteful.

Obviously, how the three cats accurately calculated the time when the cat caught the mouse did not explain. So, if the answer is not unique, then the answer can be colorful, 3, 4 or even more. If you need a unique answer, the only correct answer to this question is: this is an ambiguous question, because there is no more information about how cats catch mice, so you can't answer this question.

This simple and interesting question tells us that before solving a mathematical problem (including other problems), we must carefully understand all the information given by the topic, neither bending the meaning of the problem nor artificially attaching conditions to cater to the so-called standard answer. Of course, this interesting topic also gives us a useful inspiration in life-only cooperation can produce the best work efficiency.

2. Interesting math questions and answers

1. Three people go for 30 yuan a night. They each paid 10 yuan enough to give 30 yuan to the boss. Later, the boss said that 25 yuan was enough for today's discount, so he took out the 5 yuan and asked the waiter to return it to them. The waiter secretly hid 2 yuan's money, and then distributed the rest of 3 yuan's money to three people, each of whom gave 1 yuan. At the beginning, everyone paid 10 yuan, and now it is returned to 1 yuan, which means 10- 1 = 9. Everyone only spent 9 yuan's money, three people spent 9 yuan, 3×9 = 27 yuan+2 yuan hidden by the waiter =29 yuan. Where did the dollar go? This question caused a great response in an interview in New Zealand. Who knows the answer?

The 9 yuan money spent by each person already includes the 2 yuan hidden by the waiter (that is, the preferential price of 25 yuan+the waiter's possession of 2 yuan =27 yuan =3*9 yuan). Therefore, when calculating the composition of 30 yuan, we should not include the 2 yuan money hidden by the waiter, but should include the 1 yuan returned to everyone. Namely: 3*9+3* 1=30 yuan is just right! You can also think about it from another angle .. Those three people went out of 30 yuan and spent 25 yuan, and the waiter hid 2 yuan, so each person spent 9 yuan, plus the share of 1 yuan, which happened to be 30 yuan. So this dollar was found. Summary: This puzzle is mainly because it separates 2 yuan money from 27 yuan money. The original algorithm mistakenly thought that the 2 yuan left by the waiter privately was not included in the 27 yuan, so the wrong result was 1 yuan. In fact, this 27 yuan includes 2 yuan money left by private individuals, plus the returned 3 yuan money, and the result happens to be 30 yuan.

2, a person to buy onions, ask how much is a catty of onions. The seller said it was 1 yuan, 1 kg. This is 100 kg. The buyer also asked the seller to separate the onion from the onion. The seller said that all the people who bought onions bought them, weighed 50 Jin of onions and 50 Jin of onions, and the last one was 50*. 7 equals the lush green of 35 yuan 50*3 equals 15 yuan 35+ 15 equals that the onion buyer in 50 yuan gave the onion seller 50 yuan and left, but the onion seller was puzzled why it was 100 yuan, and why 50 yuan bought it? Why do you think this is?

1 yuan a catty answer is that green onions and green onions are one yuan a catty. When he bought green onions and green onions respectively, the weight of green onions was 7 wool and green onions were 3 wool, but the unit price changed. Green onions are less than 3 cents per catty, green onions are less than 7 cents per catty, and I bought them for 50 yuan at last.

The topic is that there is a well with a depth of 7 meters. A snail climbs up from the bottom of the well, climbing 3 meters during the day and falling 2 meters at night. How many days can a snail climb out of the well?

The answer is five days. Many people say that this problem is seven days without thinking ... In fact, in a very simple way .. you draw a piece of paper and it comes out ... This problem is very simple. ...

4. 1 yuan How many peaches can a peach eat?

The answer is 1 yuan mai 10, and there are 10 cores left after eating. Change three more peaches and eat the remaining four stones. Change 1 peach, and there are 2 stones left after eating. There are/kloc-0 peaches on credit, and there are still 3 stones left after eating. Give all the cores to the peach seller and the credit. So, you ate10+3+1+1=15 peaches. This is a well-known method ... there is another way ... don't buy ten at a time ... individually ... three for the first time ... two for the second time ... and two for the third time ... so ... it is very simple ... and it is 15.

There are twelve ping-pong balls with the same shape and size, of which only one is different in weight from the other eleven. Now it is required to weigh the ball three times with an unweighed scale, find out the ball with abnormal weight and know whether it is heavier or lighter than the other eleven balls.

The answers are divided into A B C 3 groups, with 4 in each group. For the first time, there may be three results. B or A=B or a

6. A businessman rode a donkey across the desert of 1000 km to sell 3,000 carrots. It is known that donkeys can carry 1000 carrots at a time, but eat 1 carrot every 1 km. Q: How many carrots can a businessman sell at most?

There are 534 answers. First, camel 1000 radish goes forward x 1 km, puts down 1000-2*x 1 radish, and then takes back the rest x 1 radish; Then camel 1000 radish, take x 1 radish at x 1 km, and let donkey camel 1000 radish; Continue to move forward to the distance of x2 km from the starting point, put down 1000-2*(x2-x 1) radish and return to the starting point after eating radish at x 1 km; Finally, the camel took a thousand radishes and walked to x 1, and x2 took all radishes in turn, and then walked to the end. The remaining radishes at x 1 and x2 are less than or equal to x 1 and (x2-x 1) respectively. Under the constraint of this inequality, it is enough to find the maximum of two remaining radishes, because in fact, the number of two remaining radishes is the number of radishes that can finally reach the end point. Finally, x 1=200, x2= 1600/3. The total distance traveled by the donkey is 2 * x1+2 * x2+1000 = 2466+2/3, which means that only one radish can be eaten after walking one kilometer, that is, the total number of carrots eaten is rounded to 2466, so the last radish that can be sold is 3000-2466=534.

7. The topic said that one day the pirate ship was hit by a cow that fell from the world. Five unlucky guys had to flee to an isolated island and found it lonely. Fortunately, there is a coconut tree and a monkey! Everyone picked all the coconuts and put them together, but it was late, so they went to bed first. At night, a guy got up quietly and divided the coconut into five parts. As a result, he found an extra coconut and gave it to the lucky monkey. Then he quietly hid a part, mixed the remaining coconuts together and put them back in their original places, and finally quietly went back to sleep. After a while, another guy got up quietly. Quietly divide the remaining coconuts into five parts. One coconut was given to the lucky monkey, and then one was dropped quietly. The remaining coconuts were mixed together and put back in their original place, and finally fell back to sleep quietly. Soon ... soon ... in short, all five people stood up and did the same thing. Everyone gets up in the morning and shares coconuts with ulterior motives. This monkey is really unlucky, because after dividing the coconut into five points this time, there is another coconut, so we have to give it again. The question is, how many coconuts are there in this pile?

The answer is that there are at least 1562 1 coconuts in this pile. The first person gave 1 monkey, hid 3 124 and left 12496. The second man gave 1 monkey, hid 2499 monkeys, and left 9996 monkeys. The third person gave 1 monkey and hid 1999 monkeys, leaving 7996 monkeys. The fourth person gave 1 monkey and hid 1599 monkeys, leaving 6396 monkeys. The fifth person gave 1 monkey, hid 1279 monkeys, and left 5 1 16 monkeys. Finally, everyone divided it into five parts, each 1023, and the extra 1 was given to the monkey.

8. Topic There is a treasure on an island. You see three islanders, big, medium and small. You know the big islander knows whether the treasure is on the mountain or under the mountain, but sometimes he tells the truth and sometimes he lies. Only Nakajima people know whether Oshima people are telling the truth or lying, but Nakajima people themselves tell the truth when the previous person tells the truth and tell lies when the previous person tells lies. Two islanders use their left or right hands to indicate whether or not, but you don't know which hand indicates yes and which hand indicatesno. But he always tells the truth or lies, and you don't know which of these two types he is. Can you ask whether the treasure is on the mountain or under the mountain with the least number of questions? Tip: If you ask an islander where the treasure is, he will ask how you know where it is. Equal to asking in vain)

For the sake of convenience, we will record the large, medium and small islanders as ABC (actually not C). The first question is A: Is the treasure on the mountain? The second question is B: Is A correct? The third question is B: 1+ 1 = 2, right? Ok, now the first question is, we don't know whether A answered "yes" or "no" or whether A answered "yes" or "no". We only know whether A raised his hand with his left or right hand, so we leave him alone. Look at the second question. No matter whether A's answer is "yes" or "no", as long as A's answer is correct, B will answer correctly in the second question, so he should answer "yes" (if he can speak Chinese). Still the same. No matter whether A's answer is "yes" or "no", as long as A's answer is wrong, B will also answer wrong in the second question. So anyway, B's raised hand means "yes"; The third question: since we know what the right hand means, we can determine whether A is true or false as long as we know whether B's answer just now is true or false, because the truth of both must be the same. So just ask a question, like 1+ 1=2, right? There is another way: First, ask a random person: Are you telling the truth? That person will definitely raise his hand for yes, because if he is telling the truth, he will raise his hand for yes, and if he is lying, he will also raise his hand for yes, so it can be concluded that the hand represents yes and then ask the China islanders: Did the big islanders say that the treasure is on the mountain? China islanders' answers must be correct, that is to say, the treasure is where China islanders say, because if what China islanders say is true, then what China islanders say is true, then the treasure must be on the mountain. If what China islanders say is a lie, then what China islanders say is a lie, then what China islanders actually say is that the treasure is under the mountain, but because it is false, the treasure is still on the mountain.

9. The topic says that there are many tables in a room. How many people are there? If there are three people at a table, there are two more. If there are five people at a table, there are four more. If there are seven people at a table, there are six more. If there are nine people at a table, there will be eight more. If 1 1 one table for each person, that would be just right. How many people are there in this room?

The answer is 25 19 people. As long as it is 315× (11x+8)-1,because 9 is three times that of 3, so 3 doesn't count. According to the topic, the law is 5,7. If the multiple of 9 is less than 1, then divide by the multiple of 5×7×9 = 3 1 1, and the period is 731062951840 * */kloc. Because it is divided by 1 1, there is a simple algorithm that does not need to be tried one by one. Because 3 15- 1 is divisible by 1 1, we take the periodic remainder of 1.

10, topic Someone wants to buy some tableware. After going to the tableware shop, they found that they could buy 2/kloc-0 forks and 2/kloc-0 spoons or 28 knives with their money. If the number of forks, spoons and knives he bought is not uniform, he can't match the whole set, so he must buy the same number of forks, spoons and knives, just to run out of money. What would you do if you were this person?

You can buy 12 set dishes. The price of spoon and fork is 1/2 1, the price of knife is 1/28 ... The total price of a set is1/21/28 =1/2. ...