1. When a man was walking in the forest, he overheard several robbers discussing how to share the stolen goods. The robber said that if each person divided 6 pieces of cloth, there were 5 pieces left. If everyone is divided into seven pieces of cloth, there will be eight pieces missing. Excuse me: * * How many robbers are there? How many pieces of cloth?
A: This kind of problem is the famous profit and loss problem in the history of mathematics in China. It has a fixed formula: (profit+loss)/difference = number of people (number of units). So the algorithm of this problem is: (8+5)/(7-6) = 13 (number of robbers), 13×6+5=83 (number of cloth).
2.Paige spent $65,438+0.30 on several flowerpots on Saturday. The store was having a sale that day, and everything was 2 cents cheaper. She returned the goods at the normal price on Monday and bought cups and plates. Because the price of a basin is equal to the sum of the price of a cup and a plate, she bought 16 more items than before when she went home. And because each plate is only worth 30 cents, she bought more plates than cups 10. Now I want to ask you, $65,438 +0.30, how many cups can Peggy buy on Saturday?
Answer: Paige bought 10 pots at the price of 13 cents per pot on Saturday. She returned the cans on Sunday and replaced them with 65,438+08 plates (3 cents each) and 8 cups (65,438+02 cents each), for a total price of $65,438 +0.50 (she paid 65,438 cents each).
There are four figures today. Take one of every three and add it up, and the total is 22, 24, 27 and 20 respectively. What are these four numbers?
A: If one of the numbers is X, the other three numbers are difficult to be expressed by the formula of X. The Diophantine method is very clever. He set the sum of four numbers as X. These four numbers are X-22, X-24, X-27 and X-20. Column equation (x-22)+(x-24)+(x-27)+(x-20) = X. The solution is X=3 1. 3 1-22 = 9, 3 1-24 = 7, 3 1-27 = 4, 3 1-20 = 1 1, that is, these four numbers are 9, respectively.
This is a difficult problem put forward by the famous mathematician Einstein: there is a long ladder in front of you. Step 2 at a time, and finally 1 step; If you take three steps at a time, you will eventually take two steps. If you take five steps at a time, you will eventually take four steps. If you take six steps at a time, you will eventually take five steps. Only when you cross 7 steps at a time can you complete it accurately, and there is not a step left. Please calculate, how many steps does this ladder have?
Answer: Students with strong analytical skills can see that the number of steps required should be 1 less than the common multiple of 2, 3, 5 and 6 (that is, the multiple of 30), which is the multiple of 7. So, just find a multiple of 7 from 29, 59, 89, 1 19. Soon the answer will be 1 19.
5. At the end of the Eastern Han Dynasty, a satrap was so ill that he couldn't eat, so he asked Hua Tuo to treat him. After feeling the satrap's pulse, Hua Tuo left quietly without prescription or acupuncture. The satrap thought that he was not well received, so he quickly sent a gift and invited him to dinner. Hua tuo accepts gifts and drinks, but he doesn't prescribe medicine. 10 days passed, and the satrap asked his son to ask Hua Tuo. Hua tuo, on the other hand, left with the money and left a letter. The letter cursed: "Shameless and too defensive, living in vain!" But when the satrap read this letter, his illness recovered.
What is the reason?
A: When the satrap read the letter, he was furious and repeatedly shouted, "Get him! Kill him! " The satrap chased him separately for two hours, but he didn't catch Hua Tuo. The satrap was anxious and angry, panting, coughing loudly and spitting out a pool of black blood. After vomiting, the satrap felt much more relaxed. The next day, Hua Tuo came back, returned the gift to his master and told him, "Your disease has been eradicated." It turns out that this is Hua tuo's way of making the satrap spit out blood stasis.
6. One day, King Akbar drew a line on a piece of paper and said to Bilba, "Don't cut this line off, but you must shorten it, please!" This is a difficult problem, but Bilba, who is clever and witty, solved it effortlessly.
How did he solve it?
A: Bilba immediately drew a longer line under that line and said, "Your Majesty, look, now one of your lines is shorter than this one." Akbar was speechless after reading it, because Bilba's answer met the requirements put forward by the king.
7.(nwhoii calculates the next letter) This group of letters is the second letter of a group of commonly used English words. Can you figure out what the next letter is?
NWHOII？
Answer: The first six letters are the second letter of the number 1-6, so the next letter is E.
8. If there are 9 ping-pong balls, put them in 4 bags respectively, and make sure that there are ping-pong balls in each bag, and the number of ping-pong balls in each bag is odd. Can you figure something out?
Answer: The bag of 1 contains 1, the second bag contains 3, the third bag contains 5, and then the three bags for table tennis are put in the fourth bag.
9. Mom divides the pears. If she gives 1 pear to everyone in the family, there are 1 pear left. If everyone gets two pears, there are still two pears missing. So, how many people are there in the family, and how many pears did Mom buy?
Answer: 3 people, 4 pears.
10, there are twelve ping-pong balls with the same shape and size, and only one of them is different in weight from the other eleven. Now it is required to weigh the ball three times with an unweighed scale, find out the ball with abnormal weight and know whether it is heavier or lighter than the other eleven balls.
Answer: Suppose that the ball with different mass from the other eleven balls is a ball, and its mass is greater than (or less than) the other eleven balls. Firstly, divide the 12 ball into two groups (6 balls in each group), and put the balance on the tray respectively, with the A ball on the heavy (or light) side; Then divide the six balls into two groups (three in each group) and put them on the tray respectively, and put the heavy (or light) ball A on the other side. Then put any two of the three balls on the tray respectively, and record the mass relationship, and then exchange the other ball with the ball on the tray and record the mass relationship. Then exchange the replaced ball for another ball on the tray and write down the relationship between quality and size. There is a mathematical relationship between the results.