Mathematical thinking training for the eighth grade (1)
1, there are two barrels, one is 3 kg, the other is 5 kg, and the water is infinite. How to get accurate four kilograms of water?
2. Crossing the bridge at night takes one minute for A, two minutes for B, five minutes for C and ten minutes for D ... This bridge can only carry two people at a time. You must cross the bridge with a flashlight. There is only one flashlight now. /kloc-how can four people cross the bridge in 0/7 minutes?
3. A customer came to a store in Xiao Zhao and chose goods from 20 yuan. The customer took out 50 yuan. Xiao Zhao couldn't change it without change, so he went to Han Xiao's shop next door to change 50 yuan into change, and then came back to give the customer 30 yuan change. After a while, Han Xiao came to Xiao Zhao and said that it was fake money just now. Xiao Zhao immediately replaced Xiao Li with real money. Q: How much did Xiao Zhao lose in this process?
The hen takes her children out for food. In order to prevent the chickens from getting lost, she always counts, counting from back to front to 8 and from going to back to 9. Mother hen finally counted that she had 17 children, but mother hen clearly knew that she didn't have that many children. So how many children does this confused hen have? Why did the hen count wrong?
5. Cut a large watermelon evenly with a fruit knife. If you cut 10, how many pieces of watermelon can you cut at most? How many pieces can you cut at least?
6. Xiao Li has money from 40 yuan, and he wants to buy drinks with them. The boss told him that 2 yuan could buy one bottle of drinks, and four bottles could be exchanged for one. Then, how many bottles of drinks can Xiao Li buy
7. There is a well with a depth of 4 meters and a smooth wall. There is a frog at the bottom of the well that always jumps out of the well, but this frog can jump up to 3 meters at a time. Do you think this frog can jump out of the well several times? Why?
8. Xiaohong and Xiao Li go to Xinhua Bookstore to buy books. They both want to buy the book Comprehensive Exercise, but they don't have enough money. Xiaohong is short of 4.9 yuan and Xiaoli is short of 0. 1 yuan. They bought a book with their money, but the money is still not enough. So, what's the price of this book?
9. Mingming brought a dog and two lambs home. On the way, he met a river. There is no bridge, only a boat, and the boat is very small. He can only cross the river with a dog or a lamb at a time. You can help him find a way to bring both the dog and the sheep across the river without letting the dog bite the lamb.
10. If there are 9 ping-pong balls, put them in 4 bags respectively, so as to ensure 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?
Answers to eighth grade mathematical thinking training
1. Take five Jin of water and pour it into three Jin barrels. H# }+ Pour three Jin barrels of water, and then pour two Jin of water from five Jin barrels into three Jin barrels; Then take five Jin of water and put it in three Jin barrels. The water in five Jin barrels is four Jin.
2. Party A and Party B pass first, which takes two minutes; B return, which takes two minutes; It takes ten minutes to pass the test. It takes one minute for A to return, and two minutes for A and B to return.
3. First, the customer gave Xiao Zhao 50 yuan counterfeit money, but Xiao Zhao had no change, so he changed it into 50 yuan. At this time, Xiao Zhao didn't pay. When the customer bought something from 20 yuan, because 50 yuan was counterfeit, Xiao Zhao lost 20 yuan at this time. After getting back the change, Xiao Zhao gave the customer 30 yuan, and Xiao Zhao lost 20+30=50 yuan.
4. The hen counts from the back to the front, and counts to 8, indicating that she is the eighth, and there are 7 chickens behind; The hen counted from the back to her and counted herself as 9, which means there are 8 chickens in front of her. The total number of hens' children should be 15, not 17. The reason why the hen counted wrongly is because she counted twice by herself.
5. Watermelon can be cut into pieces of 1024 at most, which is the second power of 10. At least 1 1 block.
6. First, buy 20 bottles of drinks with 40 yuan money, and you will get 20 bottles. If you exchange four bottles for one drink, you will get five bottles, then five bottles, and then 1 drink, so you will get 20+5+ 1=26 bottles.
7. This question is easy to confuse people's thinking. Most people think that frogs can jump 3 meters at a time and 6 meters twice. If they exceed the depth of the well, they can jump out of the well twice. This is not right. Because the title says "the borehole wall is smooth", which means that when a frog jumps to a height of 3 meters, it will fall back to the bottom of the well because it hits the borehole wall, so no matter how many times the frog jumps, it can't jump out of the well unless it jumps above the depth of the well at once.
8. The price of this book is 4.9 yuan. Xiaohong has no money in her pocket, and Xiaoli has 4.8 yuan in her pocket.
9. Take the dog across the river first, then return to take a lamb across the river, bring the dog back by the way, then take another lamb across the river, then return, and then take the dog across the river.
10, 1 bag, 3 bags in the second bag, 5 bags in the third bag, and then 3 bags of table tennis in the fourth bag.
The eighth grade mathematics thinking training answer (2)
1.765? 2 13? 27+765? 327? 27
Solution: Original formula =765? 27? (2 13+327)= 765? 27? 540=765? 20= 15300
2.(9999+9997+? +900 1)-( 1+3+? +999)
Solution: The original formula = (9999-999)+(9997-997)+(9995-995)++(9001-1)
=9000+9000+.+9000 (500 9000)
=4500000
3. 1998 1999? 1999 1998- 1998 1998? 1999 1999
Solution: (19981998+1)? 1999 1998- 1998 1998? 1999 1999
= 1998 1998? 1999 1998- 1998 1998? 1999 1999+ 1999 1998
= 1999 1998- 1998 1998
= 10000
4.(873? 477- 198)? (476? 874+ 199)
Solution: 873? 477- 198=476? 874+ 199
So the original formula = 1.
5.2000? 1999- 1999? 1998+ 1998? 1997- 1997? 1996+? +2? 1
Solution: Original formula = 1999? (2000- 1998)+ 1997? ( 1998- 1996)+?
+3? (4-2)+2? 1
=( 1999+ 1997+? +3+ 1)? 2=2000000。
6.297+293+289+? +209
Solution: (209+297)*23/2=58 19.
7. There are seven numbers, and their average is 18. After removing one number, the average value of the remaining six numbers is19; After removing another number, the average of the remaining five numbers is 20. Find the product of two numbers.
Solution: 7 *18-6 *19 =126-114 =12.
6* 19-5*20= 1 14- 100= 14
The two numbers removed are 12 and 14, and their product is 12* 14= 168.
8. There are seven numbers in a row. Their average is 30, the average of the first three numbers is 28 and the average of the last five numbers is 33. Find the third number.
Solution: 28? 3+33? 5-30? 7=39。
9. There are two sets of figures. The sum of 9 numbers in the first group is 63, the average of the second group is 1 1, and the average of all the numbers in the two groups is 8. Q: How many numbers are there in the second group?
Solution: Let the second group have x numbers, then 63+ 1 1x=8? (9+x)，x=3。
10. Xiaoming took part in six tests, and the average score of the third and fourth tests was 2 points higher than the previous two and 2 points lower than the latter two. If the average score of the last three times is 3 points higher than the previous three times, how many points is the fourth time higher than the third time? Solution: The third and fourth scores are 4 points more than the first two scores, 4 points less than the last two scores, and the last two scores are 8 points more than the first two scores. Because the sum of the last three times is 9 points more than the sum of the first three times, the fourth time is 9-8= 1 (points) more than the third time.
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