What does the chicken in the fortune-telling cage mean?

The most difficult problem of chicken and rabbit in the same cage

The most difficult problem of chicken and rabbit in the same cage: chicken and rabbit in the same cage, 45 heads 146 feet. How many chickens and rabbits are there in the cage?

Data expansion:

Chickens and rabbits in the same cage is one of the famous typical anecdotes in ancient China. About 65,438+0,500 years ago, an interesting question was recorded in Sun Tzu's calculation.

There are several chickens and rabbits in a cage, counting from the top, 35 heads, counting from the bottom, 94 feet. How many chickens and rabbits are there in each cage?

The essence of this problem is a binary equation. If the teaching method is proper, primary school students can understand the concepts of unknowns and equations and exercise their ability to abstract numbers from application problems. Generally, in the fourth to sixth grades of primary school, the content of one-dimensional linear equation is used to teach.

The so-called "upper position" and "lower position" refer to placing the numbers on the abacus according to the upper and lower lines. Put the number Xiao Yun 35 in the first row of the counter, put the number Xun Qing 14 in the second row, and divide the number of feet by 2. At this time, the first line 35 and the second line 47.

Subtract more half legs with a smaller head, 40 MINUS 30 (upper three divided by lower four) and 7 MINUS 5 (upper five divided by lower seven). At this time, the downlink is twelve, and thirty-five MINUS twelve (the next one is divided by three, and the next two are divided by five) to get twenty-three. At this time, the remaining calculation in the first line is the number of chickens, and the calculation in the second line is the number of rabbits.

Another simpler way to describe it is that the first one emits 35 lucky smiles, and the second one emits 94. Divide the number of feet by two, halve the number of feet with the number of heads, and subtract the number of heads from the rest. This leaves the number of chickens in the first row and the number of rabbits in the second row.

Multiply the number of feet by 2 (at this time, the coefficients of bird's feet and bird's head are exactly the same), subtract the number of feet by 2 to get the number of animals (8), multiply the number of animals by 4 (calculate the number of animals' feet), subtract the total number of feet from the number of animals and divide by 2 to get the number of birds.

If we compare the following binary equations, we will find that the ancient method is only in the right half of the equal sign of the operation equation, and does not specify what the coefficient of operation represents. Therefore, only "open-minded" people can understand immediately.