A classical Chinese math problem, classical Chinese math problem solving

I remember doing this question when I was in junior high school, and it seemed like it was supposed to be something like this:

Li Bai walked on the street without anything to do, carrying a pot to buy wine.

Double the store, see the flowers and drink a bucket.

Three encounters with shops and flowers, drink up the wine in the pot.

How much wine was in this pot?

This problem is easy to solve when you think backwards:

There is wine in the pot before the third flower: 0 + 1 = 1 (bucket).

There is wine in the pot before the third encounter: 1 2=1 2 (bucket) There is wine in the pot before the second encounter: 1 2+1=1 (1 2) (bucket) There is wine in the pot before the second encounter:

1 (1 2) 2 = 3 4 (bucket) There is wine in the pot before the first encounter with flowers: 3 4 + 1 = 1 (3 4) (bucket) There is wine in the pot before the first encounter with the store: 1 (3 4) 2 = 7 8 (bucket) column comprehensive formula:

1 2+1) 2+1 2=7 8 (bucket) At that time, I was thinking, if I did it right, Li Bai must have taken a cylinder at that time.

Set the original wine x bucket in the pot, 2[2(2x-1)-1]-1=0 solution, 2(2x-1)-1=

2x-1=x=Bucket in the pot.

Set up the original X bucket.

2[2(2x-1)-1]-1}=0

x = 7 8 Answer: There are 7 8 buckets of wine in the pot.

"Nine Chapters of Arithmetic": "Today, there are women who are good at weaving, doubling every day, weaving five feet in five days, asking how much they weave in the day? ”

There is a woman who is very good at weaving, the number of weaving per day is twice that of the previous day, and she weaves 5 feet in 5 days.

This is a proportional series problem.

The earliest to put forward and describe this mathematical problem was the topic of "things do not know the number" in the mathematical work "Sun Tzu's Arithmetic" during the Northern and Southern Dynasties. The title of this "things don't know how to count" goes like this:

There are some things that are not known in number. If you count it in threes, there are two left; If five of five are counted on the ground, there are three left at the end; If seven and seven are counted in the ground, there will be two left. Q: How many of these things are there? ”

Not as you understand it. In fact, 70 is divisible by 5 and 7 but divided by 3, 1 by 21, divisible by 3 and 7, but divisible by 5 by 1, 15 divisible by 3 and 5 but divided by 7 by 1. In the problem, this number is divided by 3 by 2, then 70 is multiplied by 2, 5 is divided by 3, then 21 times 3, 7 divided by 2, then 15 times 2, and add.

Depending on the situation, minus the multiples of the least common multiple. Subtract 105 by 2 times to get 23.

This system algorithm was obtained after the study of Qin Jiushao, a mathematician in the Southern Song Dynasty.

This is known as the Chinese remainder theorem.

Yang Zhu's younger brother is called Yang Bu, wearing a light-colored coat to go out, it rained, so Yang Bu took off the light-colored coat (it is estimated that the family is poor, afraid of getting dirty, there is no other clothes to replace, hehe), put on a dark coat and went home.

The guard dog at home didn't know, thinking it was a stranger, so he rushed up to Yang Bu, barking nonstop, Yang Bu was very angry, the consequences were very serious, and he was ready to kill the dog. His brother Yang Zhu said: "Brother, don't hit it, you are similar to it."

Wouldn't it be strange if your dog went out white and came back black? ”

]4) 2009] = -4 of the index 2009 split into 2008+1

Under the same index in 2008, multiply with -4.

1 2008)*(4)=1*(-4)=-4 choose c

Yang Zhu's younger brother was named Yang Bu and went out in white clothes. Because of the rain (wet clothes), I took off my white clothes and came back with black clothes. So their dog didn't know him anymore and yelled at him, and Yang Bu was very angry and wanted to whip him.

Yang Zhu said: "Don't fight, you are the same (with it)." Aren't you surprised that your white dog turned black some time ago? ”