Question 2: What is the law of saying defective products in math books? What is the law of finding defective products?
1, divide the items to be tested into three parts as evenly as possible (minimize the weighing times);
2. If they can't be shared equally, they will also make a difference between one more and one less 1.
3. Method: Three pieces (or three piles) of articles are randomly weighed once, and the balance: the defective products are under the balance; Unbalance: defective products are found on the balance (according to the weight or lightness given in the title).
4. Know the weighing time and find out the number of items: 3 n.
5. Know the number of items and find the number of times of weighing: take the value of n, 3 (n- 1). Question 3: Mathematics: find the third defective product. . For the first time, 4 to 4.2 to 2. 1 to 1.
Question 4: What are the rules for the fifth-grade mathematics to call for defective products? 7077679 Level 3 | My Know | Message (47) | Baidu Home Page
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What are the rules for finding defective products?
2011-6-13 20: 39 questioner: beautiful lady 1 | visits: 247 times.
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Recommended answer 2011-6-13 20: 49
The problem of finding defective products is regular.
Generally, it is divided into three parts: A, A and B. B can be equal to A, and B may also be equal to a+ 1 or a- 1, depending on the total number.
Put two A's at both ends of the balance. If the balance is balanced, the defective product is in B; If the balance is unbalanced, find out which is the defective product according to the difference between the defective product and the genuine product.
After finding it, continue to divide it into three parts.
This can eliminate two-thirds at a time, which is the fastest.
1 turn to 3, and it will be done in one go.
4-9, twice.
10-27. It takes three times.
28-8 1 takes four times.
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Question 5: math diary regularly looks for defective products and divides 10 1 coins into three piles, which are 33, 33, 35. 1 respectively. You can judge whether counterfeit money is heavier or lighter than real money by weighing it at least twice. When two piles of 33 coins are not equal, it means that 35 piles of coins are real coins. Weigh 22 coins in pile A and 1 1 coins in pile B with 33 confirmed real coins. If they are not equal, real money is heavy and counterfeit money is light; Real money is light while counterfeit money is heavy. 2. On the basis of the above problems, counterfeit money can be found only after weighing at least twice. The result of the first weighing: If pile A is heavy, the result of the second weighing: If the real money is heavy, the counterfeit money is light. According to the results of two weighing, it is confirmed that the counterfeit money is in the 1 1 coin in the B pile. The third weighing: take out 6 coins from the B pile and put them on both sides of the balance. If the three coins on the left are light, counterfeit money is among them. Fourth weighing: Take two coins on the left and put them on both sides of the balance. The balance of the day is flat, and counterfeit money is a coin that is not on the balance; The left side of the sky is light, and counterfeit money is the coin on the left side of the balance; Sunlight is on the right, and counterfeit money is the coin on the right of the balance. In all cases, counterfeit money can be determined by weighing six times. Supplement: (for reference) defective products: only 1 of n components is defective, and the weight is out of tolerance. Using a balance without weight requires weighing m (or m) times to identify defective parts. General weighing countermeasures: the balance has three states, namely, balance (=), right disk weight (↑) or right disk light (↓). N elements are divided into three piles (A, B, C), and each pile corresponds to an equilibrium state. When the overweight direction of defective products is known, the weight can be known, and the range of each weighing can be reduced to one third. When the overweight direction is unknown, it needs to be weighed again, and the number of components can be slightly increased. I don't know the weight method: when n is large, weigh it three times with a balance, and the range can be reduced to one tenth, so you can know the weight. The first, second and third results show that a = b a = c aa ≠ CD ↑ (or Cd↓) Cd A, B and Cabc=3n (defective products are in C) know that the defective products are in C and the weight of A≠C ↑ (or C ↓) Ca = C CCCD = N-9N Ca ≠ CB ≠ CB AC = NA≠baaa B+BA = C BB = BCAC knows that the defective product is in A and it is light (the defective product is in A or B) bb ≠ BC ≠ BC knows that the defective product is in B and it is heavy Bb≠Bc↓ Bb Ca, Cb, CC = naaab+ba ≠ c ? AA = ABBA knows the defective product. Divided into three piles, a = 3n, b = 3n and c = n-6n (where ca, b, c = n and cd = n-9n). Know the weight method: after the above three operations, determine the range n of defective products, and know whether the defective products are heavier or lighter than the genuine products. According to the following table, find the closest value of N'≥n in the column of "Know the weight" and determine the value of m, I wonder whether the weighing times are important or not. M M N ' N 5 243 90 4 865 438+0 30 3 27 165 438+0 2...> & gt
Question 6: 20 15 what is the next volume of fifth grade mathematics? "Finding defective products" is a kind of question in primary school mathematics, and it is also a common question in mathematics quiz. Suppose that one or more items with slightly smaller or larger mass are found in a batch of items with the same quality and appearance, which is called "defective products". Because we can't see the difference from the appearance, we can only find out the defective products by weighing. This leads to the question of "how many times can I find that/batch". Especially when the whole batch of articles consists of a large number of single pieces, it is neither practical nor necessary to weigh them one by one. At this time, the problem of "finding out the defective products with the least weighing times" has become an example object for people to study the grouping comparison law in mathematics, which is also the so-called "finding out the defective products" problem. It is not only a subject of mathematical research, but also a practical application, which is a very interesting problem.
For example, find a slightly lighter ball from a pile of nine iron balls with the same appearance, weigh it twice with an unweighed balance, and you can find it without more times.
I hope you like it.