What's the problem with geese?
It takes 7 days for a wild duck to fly from the South China Sea to Beihai, China, and 9 days for a wild goose to fly from Beihai, China. Q: If they take off from two places at the same time, how many days will they meet? This interesting question comes from China's ancient mathematical masterpiece Nine Chapters Arithmetic, which called wild ducks "geese", so it was called "geese" problem. The solution is: add two days to do divisor, multiply by dividend, and the result of division is the number of days. In 263 AD, Liu Hui, a great mathematician, explained this solution in Nine Arithmetic Notes: Wild ducks can fly the whole distance in seven days, while geese can fly the whole distance in nine days. If the least common multiple of 7 and 9 is 63, then in 63 days, wild ducks can fly 9 times and geese can fly 7 times. In other words, wild ducks and geese can fly 16 times in 63 days, or it takes 63 days for them to fly 16 times together. Then, it takes 63/ 16 (days) for them to fly together. This algorithm is very clever, and our ancestors solved the problem in proportion. They fully understand the relationship between ratio, fraction and divisor, and know that ratio is the relationship between quantity, fraction is number and division is operation, which is very remarkable.