1. Solve one of the following ten ancient Chinese math problems. Today, things are different, and three or three counts leave two. This mathematical problem was first put forward and described by Sun Tzu's Art of War in the Southern and Northern Dynasties. The topic of "things unknown" is like this: "Today, some things are unknown. If you count by twos and threes, if you count by fives, there are three left in the end; If you multiply by seven, there are two left. Q: How many of these things are there? " It's not what you understand. Actually, 70 is divisible by 5 and 7, but divisible by 3, 1, 2 1 is divisible by 3 and 7, but divisible by 5, 15 is divisible by 3 and 5, but divisible by 7, 1. If this number is divided by 3, then 70 times 2. Then multiply 15 by 2 and add .70 * 2+21* 3+15 * 2 = 233. It depends, subtract the multiple of the least common multiple of 3, 5 and 7. Subtract this question twice with 105 to get 23. This system algorithm is a mathematician in the Southern Song Dynasty.

2. Translate the following ten mathematical problems in ancient Chinese into vernacular Chinese, assuming that there are several things, two at the end of three plots, three at the end of five plots and two at the end of seven plots. How many * * * are these things?

Secondly, suppose there is a piece of land with a width of one and a half steps plus three steps, a quarter step plus five steps plus six steps plus seven steps plus eight steps (1.5+1/3+1/4+...+1/8 steps). How long does it take to measure an acre of land (240 square steps is an acre)?

Thirdly, suppose there is a wall, which is three feet thick below, two feet thick above, one foot two feet high and twenty-two feet five feet eight inches long. What is the size of this city?

Fourth, several people buy chicken together, and each person pays nine dollars, leaving eleven dollars; Six dollars each, sixteen dollars short. How many people are there and how much is the chicken?

Fifth, there is a cube with a volume of 1.86867 cubic feet. What is its side length? The ruler here is a cubic ruler. Everything with height, depth and volume is in cubic units. ), and the volume of a cube is 1953 1/8 cubic feet (1953+ 1/8 cubic feet). What is its side length? The volume of the other cube is 63,401and 512,447 cubic feet (634,065,438+0+447/565,438+02 cubic feet). What is its side length? The volume of the other cube is 1, 937,54 1, which is one seventh of 17 cubic feet (1937 541+27/41cubic feet). What is its side length?

Sixth, suppose that three bundles of excellent grain, two bundles of medium grain and one bundle of inferior grain can produce thirty-nine buckets of grain; Two bundles of excellent grain, three bundles of medium grain and one bundle of inferior grain can produce thirty-four buckets of grain; A bundle of high-grade grain, two bundles of medium-grade grain and three bundles of low-grade grain can produce 26 buckets of grain. How much food can the upper, middle and lower crops produce per bundle?

Seventh, suppose there is a 10-foot-long square pool with reeds growing inside, one foot above the water. Pulling the reeds to the shore is exactly equal to the pool shore. How deep is the water and how long is the reed?

Eighth, suppose there is an isosceles trapezoid with a base length of 20 steps, a top length of 5 steps and a height of 30 steps. What is the area of this land? There is also an isosceles trapezoid with a base length of 1 17 steps, a top length of 50 steps and a height of 135 steps. What is the area of this land?

Ninth, suppose there are five people, doctor, Bu Geng, Ba Mao, Shang Zao and male scholar, hunting five deer. I'm going to divide the prey by title and ask everyone how much to take.

Tenth, suppose it takes eight days for Jia county to collect grain and transport it to ten thousand households; 9500 households in county B, transported for ten days; County C 12350 households, and the transportation takes thirteen days. Dingxian12,200 households, transported for 20 days. The four counties collected 250,000 tons of grain, and the grain for automobiles was 1 10,000 tons. If the grain is collected according to the distance of the road and the proportion of households, how much grain will be collected by each household in each county and transported by each vehicle?