The most mathematical solution

1. There is something unknown in Sun Tzu's Art of War.

Three three two,

Three fifths,

Seven and seven have two left.

Ask geometry?

Translation? There is a pile of goods, three with two left, five with three left and seven with two left. Ask the quantity of this pile of goods? "

The total number of terms is not unique, but the arithmetic progression with a difference of 3*5*7= 105. Each answer can be decomposed into the sum of three numbers. 1 This number can be divisible by 5 and 7. After dividing by 3, the remainder is 2. The second number can be divisible by 3 and 7, and the remainder is 3 after division by 5; The third number is divisible by 3 and 5, and the remainder is 2 after division by 7. It is easy to see that the number 1 is 140, the second number is 63, and the third number is 30, so 140+63+30=233 is a solution of the original question, and 23, 138, 233 and 338 are all.

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2. There are pheasants and rabbits in the same cage under the volume of Sunzi Shujing.

There are 35 heads on the table,

It's 94 feet below,

Excuse me, the geometry of pheasant rabbit?

There are chickens and rabbits in a cage today, with 35 heads above and 94 feet below. How much are chickens and rabbits?

Solution (one of arithmetic solutions) takes rabbit's foot as the main element;

Assuming that the head 35 is all rabbits, there should be 35×4= 140 feet, so there are 46 extra feet. Rabbits can be used instead of the same number of chickens to reduce the number of feet. How many rabbits (that is, how many chickens) need to be removed to reduce the number of feet? obviously

Chicken 46÷2=23 (only)

Rabbit 35-23= 12 (only)

If calculated by mathematical comprehensive formula:

Chicken (35×4-94)÷(4-2)=23 (only)

Rabbit 35-23= 12 (only)

Answer: 23 chickens and 0/2 rabbits.

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3. Mei Ai became a monk in the "unified school of addition and subtraction algorithms".

A hundred and eight thousand miles.

75 times a day,

How many days do you need to return?

In the Tang Dynasty, Sanzang went to the Buddhist holy land for Buddhist scriptures and walked 108000 Li, with an average of 75 Ali days. How many days will Tang Priest and his party come back?

solution

108000÷75= 1440 (days)

So it takes 1440÷360=4 (years) to reach the Western Heaven.

The round trip time is 2×4=8 (year).

A: Tang Sanzang went to the Western Heaven four years later and returned on 1440 eight years later. It's very simple!

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4. Mei Chengcheng's "Addition and subtraction algorithm", a hundred rabbits entered the camp.

How many men and women are fighting.

It's hard to take one person at a time,

Four people and three people must stop.

Get together, make trouble,

Everyone can catch it and go home.

If Yingxian can figure it out,

How many people commented.

There are 65,438+000 rabbits running into Shannomura from all directions, and men and women are scrambling to catch rabbits. If there are/kloc-0 rabbits, there are only/kloc-0 rabbits. If you give four rabbits to three people, it will be equally divided. The men and women who caught the rabbit were very happy and shouted happily. I saw everyone walking home with the rabbits they caught. Smart people come to calculate, how many men and women catch rabbits?

Solution 1: If four rabbits are divided into one group, there are 100 rabbits * * * 100÷4 = 25 (group). Since there are three rabbits in a group, there should be 25×3=75 rabbits in 25 groups.

A: * * * A total of 75 people.

Solution 2 (ancient calculator solution) List the comprehensive formulas according to the meaning of the question:

100 4× 3 = 75 (person)

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5. Yang Hui's Daily Algorithm finds the interval 625,

Second, seek abdication. One, two, five,

Three requests, 1875,

Fourth, change it to 25,

Three, one, two, five, yes,

Six, ask for two prices, three seven five,

Seven four, three, seven, five,

Eight to five.