The problem of keeping chickens and rabbits in the same cage is one of the famous and interesting topics in ancient China. About 1500 years ago, this funny question was recorded in Sun Tzu's calculation. The book describes it this way: Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. The geometry of chicken and rabbit? These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage? Can you answer this question? Do you want to know how to answer this question in Sunzi Suanjing?
The answer is this: If you cut off the feet of every chicken and rabbit in half, then every chicken will become a "one-horned chicken" and every rabbit will become a "two-legged rabbit". In this way, the total number of feet of (1) chickens and rabbits changed from 94 to 47. (2) If there is a rabbit in the cage, the total number of feet is more than the total number of heads 1.
So the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, that is, 47-35 = 12 (only). Obviously, the number of chickens is 35- 12 = 23.
This idea is novel and strange, and its "foot-cutting method" has also amazed mathematicians at home and abroad. This way of thinking is called reduction. Reduction method means that when solving a problem, we do not directly analyze the problem first, but deform and transform the conditions or problems in the problem until it is finally classified as a solved problem.
extreme
If there is a pond with a lot of water in it, and there are two empty kettles, which can hold 5 liters and 6 liters of water respectively, how can you use these two kettles to get 3 liters of water from the pond? The answer is: first fill a five-liter kettle with water, and then pour it into a six-liter kettle. At this time, pour some five liters of water into a six-liter kettle, and the six-liter kettle will be full. At this time, there are still four liters of water in the five-liter kettle. Then pour the water out of the six-liter kettle and pour five liters of water into the six-liter kettle. At this time, there are only four liters of water in the six-liter kettle. Then fill the five-liter kettle and put it in the six-liter kettle. Then the 6-liter kettle is full. At this time, there are only three liters of water left in the five-liter kettle.
A farmer took three rabbits to the market. Each rabbit weighs about 3~4 kilograms. However, the farmer's scale can only weigh 5 kilograms. What do farmers call it?
The answer is: first weigh the three together, then take out one, and calculate the difference after weighing.
Tisso
Recently, a new waiter came to the "Mathematics Store". It is Xiao's Four. One day, Little "3" went to the math shop and bought a pencil. The little "4" said, "You have to pay 1 54 yuan."
Little "3" paid 1 yuan 50 cents and asked, "How can I pay 4 cents?" Little "4" quickly said, "You don't have to pay the 4 cents." Little "3" asked doubtfully, "So you're not going to suffer?" "No, this is a rule of our shop, called" rounding ". Anything less than 4 cents is discarded. If it is more than 50 cents, it will be 1 dime. " Little "4" kindly explained. Little "3" said happily, "Thank you, that's very kind of you!"
"Yes, I like 4 too." "25" ran over and said, "Because 25×4= 100, it is relatively simple to calculate, for example, 25×87×4=25×4×87, isn't it fast and simple to calculate? ! "
"Yes, really fast and easy. I also like 4. " It turned out to be "29" "25" quickly asked, "Hey, how can you like' 4'?" "No.29" said unhurriedly, "You don't understand this. Generally speaking, February is 28 days. February is only 29 days when the Gregorian calendar year is a multiple of 4. I only get one chance every four years. Sure, I like' 4'. However, the Gregorian calendar year is one hundred, and it must be a multiple of 400. There are only 29 days in February. This year is called leap year. "
"Ah, the use of' 4' is really great!" "25 exclaimed.
This "4" waiter is really a very gentle and likable waiter.