1, leopards and lions compete in the round trip of 100m. The leopard is 3 meters long and the lion is 2 meters long, but the leopard can run 2 steps and the lion can run 3 steps. Who won?
Analysis and solution: the leopard runs 3×2=6 meters in two steps, and the lion runs 2×3=6 meters at the same time, both of which have the same speed. However, since 100m is exactly 50 times that of 2m, that is, the lion runs 50 steps at 100m and the leopard runs at 1m 100÷3=33 steps, so the remaining 1m has to run one step. Therefore, the lion won.
There is a well 9 meters deep. Snails and turtles climb up from the bottom at the same time. Because the shaft wall is slippery, the tortoise climbs 3 meters during the day and drops 1 meter at night; Snails climb 2 meters during the day and drop 1 meter at night. Q: When the tortoise climbed to the wellhead, how many meters was the snail from the wellhead? Analysis and solution: The tortoise climbs 3m during the day and descends 1m at night, that is, it climbs 2m every day. But the climbing height on the last day was 3 meters, so it took the tortoise (9-3) ÷ (3- 1)+ 1 = 4 days to climb to the wellhead. However, the snail only rises 2- 1 = 1 m every day, because the tortoise climbed the wellhead during the day on the fourth day, so the snail should not consider "falling at night 1 m" on the fourth day, when the snail was 9-(4+1) = 4m away from the wellhead.
Party A and Party B run the 3000m race. When Party A is 500 meters away from the finish line, Party B is 600 meters away from the finish line. Run like this. When A reaches the finish line, how many meters is B from the finish line?
Analysis and answer: According to the meaning of the question, A runs 3000-500 = 2500m, while B can only run 3000-600 = 2400m, that is, A runs 25m and B runs 24m. Because 500 meters includes 20.25 meters, that is, A can reach the finish line after running 20.25 meters, and B can only run 20.24 meters, so B is still 600-24× 20 = 120 meters from the finish line.
4, broken car down the mountain
A broken car has to walk two miles, one mile up the hill and one mile down the hill. When it goes uphill, the average speed is 15 miles per hour. How quickly can you reach an average speed of 30 miles per hour on the second mile? Is it 45 miles? You have to think about it!
Answer: In any case, the average speed of a broken car is less than 30 mph. Because when the average speed is 30 miles per hour, the total time for the broken car to go up and down the mountain should be115 hours. It took115 hours to climb the mountain. So the average speed of broken cars is less than 30 miles per hour.
5. How many eggs does * * * sell?
Mrs. Wang went to the market to sell eggs. The first man bought half the eggs in the basket one after another, and the second man bought the remaining half. At this time, there is an egg left in the basket. How many eggs did Mrs. Wang sell?
Answer: 10.
6. How many people took the exam?
There are six multiple-choice questions on the test paper, and each question has three options. As a result, the marking teacher found that three answers were randomly selected in all the test papers, and the choice of one question was different from each other. How many people will take the exam at most?
Answer: 13 people at most.
7. A family of three has a picnic outdoors with a barbecue grill, which can just accommodate two barbecues. Ask how to roast three pieces of meat in the shortest time. Father: "A piece of meat should be roasted for 20 minutes on both sides, because it takes 10 minutes on each side." Bake two pieces at the same time, and it takes 20 minutes to finish baking two pieces. Bake the third slice for another 20 minutes, and it will take 40 minutes to bake it all. Daughter: Dad, I can save 10 minutes. "Let the pieces of meat be A, B and C, and the two sides of each piece of meat are marked as 1 and 2. Bake A 1 and b 10 minutes before1. Put the meat piece B aside first, then bake A2 and C 1 bake 10 minutes, and then the meat piece A can be finished. It took 10 minutes to roast B2 and C2, while it took only 30 minutes to roast three pieces of meat. This belongs to the problem of overall planning in mathematics. The crux of the matter is that there is no need to roast the reverse side of the slice immediately after roasting the first side.
8. It takes four people to cross the bridge 1 minute, 2 minutes, 5 minutes, 10 minutes. As it was dark, they had to use flashlights to cross the bridge, but they always had only one flashlight. The load-bearing capacity of the bridge was limited, and at most two people could cross it at a time. How can I cross the bridge in the shortest time? It's easy to think that A and B, C and D should be time-saving. There is only one flashlight, and only two people can pass by at a time, so one person has to go back to deliver the flashlight after crossing the bridge. In order to save time, people must undertake the task of sending flashlights back and forth as soon as possible. Then you have to let Party A and Party B cross the bridge first, which takes 2 minutes, then Party A returns to send flashlights, which takes 1 minute, and then Party C and Party D cross the bridge together, which takes1minute. Next, B returns, sends a flashlight, which takes 2 minutes, and then crosses the bridge with A, which takes another 2 minutes. So the total time is: 2+1+10+2+2 =17 minutes.
9. Pancake question: Mom needs two minutes to bake one cake, one minute to bake the front and back, and at most two cakes are put in the pot at the same time. How many minutes does it take to bake three cakes at least?
10, socks problem, there are five pairs of socks of different colors in the drawer, and the lights are not turned on. How many socks do you need to pull out of a pair of socks of the same color at most?
1 1. Egg problem: Xiao Zhang sells eggs and a basket of eggs. The first person comes to buy half, and Xiao Zhang gives him another one. The second person buys half, and Xiao Zhang gives him another egg. The third person buys half and Xiao Zhang gives him another one. The fourth person buys half and Xiao Zhang gives him another one. The eggs have just been eaten! How many eggs has Xiao Zhang always had?
12, table problem, an square table, how many corners are there after cutting off a corner?
13, cut tofu question: How many pieces can a piece of tofu be cut three times at most?
14, watermelon cutting problem: three knives cut 7 petals, eat the remaining 8 skins, how to cut?
15, bamboo pole problem: Can a 5-meter-long bamboo pole pass through the door of 1 meter high?
16, carton problem: Can a square box with a side length of one meter put down a wooden stick of 1.5 meter?
17, clock problem: 12 hours, how many times does the clock and minute hand repeat?
18, children line up, Xiaohong ranks seventh from left to right, and Xiaohong ranks eighth from right to left. How many people are there in this line?
Answer: There are 14 children in this line.
19, to be honest: 8 children played hide-and-seek and 4 children were caught. How many are left?
Answer: There are three left. (Explanation: Eight children play hide-and-seek, one is an eagle and only seven are chickens. After four children were arrested, there were three left. )
20, there are two cups of juice, the baby drank half a cup first, and the mother filled it up again; The baby drank another half cup, and the mother filled it again. Finally, the baby drank it all. How many cups did the baby drink?
The above are the math problems I sorted out, I hope I can help you.