Hypothesis (popular): suppose chickens and rabbits listen to instructions and let all animals lift one foot.
Feet standing in a cage: 94-35=59 (only)
Then lift one foot, lift both feet, and the chicken will fall down, leaving only the rabbit standing on two feet.
Standing feet: 59-35=24 (only)
Rabbit: 24÷2= 12 (only)
Chicken: 35- 12=23 (chicken and rabbit are in a cage) is an ancient mathematical problem. At first, it was devoted to the quantitative relationship between the head, feet and number of chickens when chickens and rabbits were mixed. People often use hypothetical methods to answer such questions. But if chickens and rabbits are given new life, we will get unexpected solutions.
Example: There are 50 chickens and 140-foot rabbits today. How many chickens and rabbits are there?
Analysis and solutions:
Method (1)
Let each chicken stand on one foot and each rabbit stand on two hind feet, then the total number of feet on the ground is only half of the original, that is, 70 feet. The number of feet of a chicken is the same as the number of heads, while the number of feet of a rabbit is twice that of a rabbit. So, 70 MINUS the number of heads leaves 70-50 = 20 rabbits and 50-20 = 30 chickens.
The golden rooster is independent and the rabbit stands up-what a clever idea!
Method (2)
Let each rabbit grow another head and then split into two "half rabbits" with "one head and two feet". Half rabbits and chickens have two feet, so * * * has 140÷2=70 chickens and rabbits, and 70-50 = 20 rabbits, which is the number of rabbits (because each rabbit becomes two').
Divide the rabbit into "half rabbits"-brilliant idea!
Method (3)
If each chicken's two wings are feet, then each chicken has four feet, just like the rabbit's feet. Then the chicken and rabbit have 50×4=200 feet, which is 200- 140 = 60 feet. This is the number of chicken wings, so the chicken has 60÷2=30 feet and the rabbit has 50 feet.
Think of chicken wings as feet-good idea!
Method (4)
Let every chicken and rabbit have "special functions". The chicken flew and the rabbit stood up. At this time, all the feet standing on the ground are rabbits, and its number of feet is 140-50× 2 = 40, so the number of rabbits is only 40÷2=20, and then we know that there are 30 chickens.
Chickens and rabbits have "special functions"-think more wonderfully!
Students, do you have any thoughts after reading these four schemes?
Elementary school math: chicken and rabbit are in a cage.
Have you ever heard of the problem of "chickens and rabbits in the same cage" This question is one of the famous and interesting questions in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. The book describes it like this: "There are chickens and rabbits in the same cage today, with 35 heads on the top and 94 feet on the bottom. 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.