2. There are 1000 boxes of products with the same appearance, of which 999 boxes are of the same weight, and 1 box is less defective. Now that we have a scale (which can weigh 500 boxes at a time), how can we find out the defective box as soon as possible?
There are eight balls, one of which is lighter. Put these balls on the balance and weigh them several times. Can you find the light ball and write the method?
There are five bags of salt, four bags are 500g each, and the other bag is not 500g, but I don't know whether it is heavier or lighter than 500g. How do you weigh it with a balance? Please write down the process.
5. Mom bought 500 grams of wool (10 rolls), one of which was less than 50 grams. If you weigh it with a balance, how many times must you weigh it at least to ensure that a defective roll is found?
6. There are nine steel balls, eight of which have the same weight, and the other one is slightly lighter than these eight. Can you find a lighter steel ball by weighing it at least several times?
7. There are five boxes of table tennis, each with 6 balls. The boxes and balls have the same appearance. Among them, 4 boxes are qualified, each ball weighs 2.7 grams, and the other box is unqualified, each ball weighs 2.5 grams. Please design a method that can be opened for inspection, and it only takes one time to point out which box contains unqualified products.
8. There are 9 nuts, one of which is defective and light. The balance is used now, at least weigh it.
Only once can we find this defective product.
9. There is a balance and nine weights, one of which is lighter than the other eight. How many times do I have to say it before I can find the lighter one?
10, there are nine coins with the same appearance, and one counterfeit coin is heavier than the real one. How many times can you find fake coins by weighing them with a balance? Please write down the process.
1 1, Yi * * * has 200 coins, of which 199 coins have the same weight, and the other one is lighter than the others. Now I have a balance in my hand. If you can only weigh it five times at most, can you find a lighter coin? If not, please explain why, if yes, please give a name.
12, with 10 nuts, one of which is defective and lighter. Now use the balance. Please find out this defective product and write your own method.
Candy 13 boxes, of which 12 boxes have the same quality, and the other box is missing a few sweets. If you weigh it with a balance, how many times can you find this box of candy? Please write down the process.
14. There are 7 coins with the same appearance, and 1 counterfeit coin is heavier than the real coin. How many times can counterfeit money be found by weighing it? Please write down the process.
15, there are four piles of balls with the same appearance, each pile has four. It is known that three piles are genuine and one pile is defective. Each quality ball weighs 10g, and each quality ball weighs11g.. Please weigh it with a balance and find out the defective pile.
16. A box of oranges 15 bags, of which 14 bags have the same quality, and the other 1 bags are insufficient and light. How many times can you guarantee to find this bag of oranges at least? Please try to show the weighing process with a chart.
17.729 small bearings, one is defective, lighter than the qualified bearing, and the rest are of the same weight. What is certain now is that this defective product can be weighed at least several times with unmarked scales.
18, 50 gold coins, one of which is counterfeit, and the appearance is the same as the real one. Just a little lighter than the real thing. Can you find counterfeit money by weighing it four times without weight?
19. Gold coins 10 bags, only one of which is fake. Each real gold coin weighs 10g, each fake gold coin weighs 9g, and each bag weighs 100 gold coin. How many times must I weigh it to find the fake gold coins?
20. To find out 1 item from 3 items, you must weigh it with a balance at least twice to find it.
2 1, there are 10 boxes of parts, one of which is defective, and each part in the defective box is lighter than the standard mass 10g. Due to the carelessness of the administrator, it is difficult to tell which box it is. Can you weigh it with a balance and find out the defective products in that box?
22. One of the 60 parts is unqualified, which is lighter than other parts. The quality inspector should weigh it with a balance at least several times to ensure that this unqualified part can be found. Please use a chart to show the process of finding defective products. )
23, 9 ancient coins, one of which is lighter, can't be found by weighing it twice.
24. There are 15 boxes of biscuits with the same size and package, of which 14 boxes have the same quality, and 1 box is missing some biscuits. If you can weigh them with a balance, how many times can you find out this box of biscuits?
25.( 1) Fill in the table below to see what is good.
The number of diamond rings is divided into the number of copies and the number of times of weighing, which ensures that fake diamond rings can be found in the number of times of weighing.
1 1 3(4,4,3)
1 1 3(5,5, 1)
1 1 4(3,3,3,2)
1 1 4(2,2,2,5)
(2) According to the above table, how many times does it take to find a fake diamond ring?
26. There are 29 boxes of biscuits, 28 boxes are of the same quality, and a few pieces are missing from 1 box. How many times can you find this box of biscuits if you can weigh it with a balance?
27. Among the18 parts, there is one unqualified part, which is lighter than other parts. The quality inspector should weigh it with a balance at least several times to ensure that this unqualified part can be found. Please use a chart to show the process of finding defective products. )
28. There are three tennis balls, each with 12 balls, of which 1 defective balls are heavier than the genuine ones. Now, you only need to weigh them three times with a balance without weight to find out the defective ball. Can you guarantee to find it?
29. There are only 5g and 30g weights left in an old balance. Xiao Ming wants to use this old balance to divide 300g of medicine into three parts with the least number of times. How many times does Xiaoming have to weigh himself?
30. There are 10 1 coins, of which 100 is homogeneous and the other is counterfeit. It is unknown whether counterfeit money is heavier or lighter than real money.
(1) With the balance, how many times can I weigh counterfeit money to judge whether it is heavier or lighter than real money? Tell me your name.
(2) According to the above question, how many times can you find counterfeit money at least?