Someone asked him how long it would take to demonstrate this problem, and he said, "All Sundays in three years". Please answer quickly. How many days did it take him at least?
2. the king's reward
Legend has it that Indian King Shehan intends to reward Sass Bandal, the inventor of chess. The wise minister knelt before the king and dared to say, "Your Majesty, please give me a grain of wheat in the first box, two grains in the second box and four grains in the third box. At this speed, each compartment is twice as big as the previous one. Your Majesty, give all the 64 grains of wheat like this on the chessboard to the servant? " The king said, "Your request is not high, and you will get it." . With that, he ordered a bag of wheat to be taken to the throne, and the work of counting wheat grains began. ..... Before the 20th cell, the bags were empty, and bags of wheat were transported to the king. However, the number of wheat grains increased rapidly one after another, and it soon became clear that even if all the food in India was taken out, the king could not fulfill his promise to the inventor of chess. Calculate, how many grains of wheat should the king give to the chess inventor?
3. The prince's math problem
Legend has it that there was once a prince. One day, he called his sisters together and gave them a math test. The title is: I have two jewelry boxes, gold and silver, which contain several pieces of jewelry. If I give 25% of the jewels in the gold box to the first person who solves this problem correctly, I will give 20% of the jewels in the silver box to the second person who solves this problem correctly. Then I took five pieces from the gold box and gave them to the third person who got the title, and then took four pieces from the silver box and gave them to the fourth person who got the title. Finally, I lost 10 pieces of jewelry left in the gold box, and the ratio of the remaining pieces in the silver box to the divided pieces was 2: 1. Can anyone figure out how many jewels were in my gold box and silver box?
4. The princess asked a question.
In ancient times, it is said that Princess Lubusha of the Czech Republic wrote such an interesting question: "How many plums are there in a basket? Give half of them to the first person, the other half to the second person and the last half to the third person. Then there are no plums in the basket. How many plums are there in the basket? "
5. Goldbach conjecture
Goldbach was a German mathematician more than 200 years ago. He found that every even number greater than or equal to 6 can be written as the sum of two prime numbers ("1+ 1" for short). Such as: 10 = 3+7, 16 = 5+ 1 1 and so on. He tested many even numbers, which showed that this conclusion was correct. But he can't prove that this conclusion is correct in theory. 1748, he wrote to Euler, a famous mathematician at that time, asking him to give directions. Euler wrote back that he thought this conclusion was correct, but he couldn't prove it. Because it is not proved theoretically that it is only a conjecture, the problem raised by Goldbach is called Goldbach conjecture.
Many mathematicians in the world have made great efforts to prove this conjecture. From "1+4" to "1+3" to 1966, China mathematician Chen Jingrun proved "1+2". That is to say, any large enough even number can be expressed as the sum of two numbers, one of which is a prime number and the other is either a prime number or a product of two prime numbers.
Can you write the following even numbers as the sum of two prime numbers?
( 1) 100=
(2)50=
(3)20=
6. Bijuk's seven sevens
At the beginning of the 20th century, the British mathematician Bewick discovered a special division problem. Please complete this special part.
7. The epitaph of Diao Fandu
Diao Fan, a mathematician in the third century A.D., wrote on his epitaph: "The capital of Diao Fan is buried here. The epitaph tells you that one sixth of his life is a happy childhood and one twelfth is a happy youth. He was married but had no children, so he spent another seventh of his life. Five years later, he will have a son; It's a pity that my son only lived half his father's life and died four years earlier than his father. How long did Diao Fan live?
8. Will (male name)
Legend has it that when the ancient Romans died, they wrote a will to their pregnant wife: if they gave birth to a son, they would give 2/3 of the inheritance to the son and mother1/3; If the baby is a daughter, give 1/3 of the inheritance to the daughter and 2/3 to the mother. As a result, my wife gave birth to a boy and a girl. How to distribute it to meet the requirements of the will?