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.
The solution in Sun Tzu's calculation is ingenious. It is calculated according to the formula: the number of rabbits-the number of heads. The specific calculation is as follows: number of rabbits (only), number of chickens = number of heads-free number = 35- 12 = 23. The origin of the formula is given in the book: after the number of feet is divided by 2, each chicken has only one foot, and each chicken has only one foot.