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标题: 国内小学五年级的数学题！ [打印本页]
作者: berriuqam    时间: 2004-11-17 21:51
标题: 国内小学五年级的数学题！
100个人回答五道试题，有81人答对第一题，91人答对第二题，85人答对第三题，79人答对第四题，74人答对第五题，答对三道题或三道题以上的人算及格，那么，在这100人中，至少有（ ）人及格。

请说出算法！不准列方程,要用小学算术的水平解这道题.
作者: huck    时间: 2004-11-17 22:40
This is not a difficult question for many kids but may remain to be difficult  for the whole liives of many others. The key is to understand when the worst case occurs in terms of the failure rate. I believe chinese students have only a slight advantage in this question as compared to whites.
作者: dengyi0517    时间: 2004-11-17 23:32
标题: 0个
至少0个人不及格,对不?因为一共错了90个题,平均一个人错的还不到1个,所以平均都及格了,既然平均都及格了,那就至少0个人不及格
作者: GiganticBalls    时间: 2004-11-17 23:33
HI:cool:

没答对第一题的有100-81=19
没答对第二题的有100-91=9
没答对第三题的有100-85=15
没答对第四题的有100-79=21
没答对第五题的有100-74=26
五题全错最多有9个人；

去掉这9个人----
没答对第一题的有19-9=10
没答对第三题的有15-9=6
没答对第四题的有21-9=12
没答对第五题的有26-9=17
四题全错的最多有6个人；

去掉这9+6=15人----
没答对第一题的有19-15=4
没答对第四题的有21-15=6
没答对第五题的有26-15=11
三题全错的最多有4个人；

不及格的最多有9+6+4=19人，
则及格的最少有100-19=81人。
作者: berriuqam    时间: 2004-11-18 00:00
标题: 很棒的答案
Post by GiganticBalls
HI:cool:

没答对第一题的有100-81=19
没答对第二题的有100-91=9
没答对第三题的有100-85=15
没答对第四题的有100-79=21
没答对第五题的有100-74=26
五题全错最多有9个人；

去掉这9个人----
没答对第一题的有19-9=10
没答对第三题的有15-9=6
没答对第四题的有21-9=12
没答对第五题的有26-9=17
四题全错的最多有6个人；

去掉这9+6=15人----
没答对第一题的有19-15=4
没答对第四题的有21-15=6
没答对第五题的有26-15=11
三题全错的最多有4个人；

不及格的最多有9+6+4=19人，
则及格的最少有100-19=81人。

蒙城还是牛人多啊,在其他论坛上这道题的答案五花八门
作者: beauchemin    时间: 2004-11-18 00:31
答对三道题就及格，所以，只要在答对四道题的人中选择，最大的三个数，然后再最大的三个数中选择最小的81，这道题根本不用算。我五岁就玩过。一百匹马，一百块瓦，大马驮仨，小马驮俩，最少多少趟能运完所有的瓦？？这才好玩！
作者: beauchemin    时间: 2004-11-18 00:34
一百匹马，一百块瓦，大马驮仨，小马驮俩，最少多少次运完所有的瓦？
作者: berriuqam    时间: 2004-11-18 01:01
Post by beauchemin
一百匹马，一百块瓦，大马驮仨，小马驮俩，最少多少次运完所有的瓦？  
没搞懂题目.一百匹马，一百块瓦.那不是1块瓦/马.就都是小马也不要一次啊.
作者: huck    时间: 2004-11-18 09:53
标题: To the answer above
Yes your answer is right. But do you think a primary scho0l pupile would provide such a lengthy answer?
If you understand that the largest number of students fail when they all had been wrong in exactly three questions and all others had perfect answers for all the questions. It is just a piece of cake. Well, there may be cases that 3 does not divide the total number of incorrect answers  as in the case of this question, you just round the result to the immediately smaller integer. In such a case, there is one or two students who passed didnt have the perfect score.
作者: oldwolf    时间: 2004-11-18 10:03
标题: A simple algorithm to solve it.
Here is a simple algorithm to solve it.


The persions who didn't answer correctly the first question: 19
second : 9
third : 15
fourth: 21
fifth: 26


Sort the above numbers:

9
15
19
21
26

Take the last 3 numbers: 19 21 26.

The minimum of the last 3 numbers is the answer: 19.


This algorithm can be applied to other questions like 1000 students answer 50 questions and can be quickly and easily solved in a computer.


This question is a good one to test students studying computer algorithms.


Oldwolf
Post by berriuqam
100个人回答五道试题，有81人答对第一题，91人答对第二题，85人答对第三题，79人答对第四题，74人答对第五题，答对三道题或三道题以上的人算及格，那么，在这100人中，至少有（ ）人及格。

请说出算法！不准列方程,要用小学算术的水平解这道题.
作者: oldwolf    时间: 2004-11-18 10:03
标题: A simple algorithm to solve it.
Here is a simple algorithm to solve it.


The persions who didn't answer correctly the
first question: 9
second : 15
third : 19
fourth: 21
fifth: 26


sort the above numbers:

9
15
19
21
26

Take the last 3 numbers: 19 21 26. The minimum of the these 3 numbers is the answer: 19


This algorithm can be applied to other questions like 10000 students answer 1000 questions and can be easily solved in a computer.

Post by berriuqam
100个人回答五道试题，有81人答对第一题，91人答对第二题，85人答对第三题，79人答对第四题，74人答对第五题，答对三道题或三道题以上的人算及格，那么，在这100人中，至少有（ ）人及格。

请说出算法！不准列方程,要用小学算术的水平解这道题.
作者: oldwolf    时间: 2004-11-18 10:03
标题: A simple algorithm to solve it.
Here is a simple algorithm to solve it.


The persions who didn't answer correctly the first question: 19
                   second        : 15
                   third           

Post by berriuqam
100个人回答五道试题，有81人答对第一题，91人答对第二题，85人答对第三题，79人答对第四题，74人答对第五题，答对三道题或三道题以上的人算及格，那么，在这100人中，至少有（ ）人及格。

请说出算法！不准列方程,要用小学算术的水平解这道题.
作者: cliff2002    时间: 2004-11-18 10:12
标题: Does not make any sense
The kind of question remind me 高中语文的文章 <<孔以及>> 中 ”回香豆的回有几种写法”。
except for very small number of extradinary students, most students just memorize the steps instructed by teachers,ths kind of education will sacrifice all other kinds of capacity such as imagination, creativity, humanity...


Remember what Chinese lack most is "innovation" , even chinese students gained 100 in test, so what?
作者: oldwolf    时间: 2004-11-18 10:34
标题: A simple algorithm to solve it.
A quick answer to other quesitons:

The maximum number of students who failed 4 questions is: 15


The maximum number of students who failed 5 questions is: 9


Post by oldwolf
Here is a simple algorithm to solve it.


The persions who didn't answer correctly the first question: 19
second : 9
third : 15
fourth: 21
fifth: 26


Sort the above numbers:

9
15
19
21
26

Take the last 3 numbers: 19 21 26.

The minimum of the last 3 numbers is the answer: 19.


This algorithm can be applied to other questions like 1000 students answer 50 questions and can be quickly and easily solved in a computer.


This question is a good one to test students studying computer algorithms.


Oldwolf
作者: berriuqam    时间: 2004-11-18 10:41
发此帖纯属娱乐,和打麻将没什么区别,您认为腰酸背疼的打一晚上麻将有何意义?请大家把精力集中在解法上,题外话不要多谈了.
作者: huck    时间: 2004-11-18 10:45
标题: reply to oldwolf
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: oldwolf    时间: 2004-11-18 12:45
标题: The answer is 70
Here is why it should be 70.


The total wrong answers is

9+15+19+21+26 = 90

The maximum number of studnets who failed 3 questions could be 90 / 3 = 30

In this case, it is possible that 30 students failed the exam. The following is how the distribution of wrong answers are.


wrong
answers

9 =   5    0    0       4     0
15= 0    6    0       4     5
19= 0    0    10     4     5
21= 5    6    10     0     0
26= 5    6    10     0     5

total
failed
students 5 + 6 + 10 + 4  + 5   = 30


Therefore, the maxium number of failed students is 30. So at least 100 - 30 = 70 students pass the exam.


But just in this case, the maximum number of failed students ncould be 30. If the distribution of failed question changes, it is possible the maximum number clouldn't reach 30.







Post by huck
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: oldwolf    时间: 2004-11-18 12:45
标题: The answer is 70
Here is why it should be 70.


The total wrong answers is

9+15+19+21+26 = 90

The maximum number of studnets who failed 3 questions could be 90 / 3 = 30

In this case, it is possible that 30 students failed the exam. The following is how the distribution of wrong answers are.


wrong
answers

9 =    5    0    0       4     0
15= 0    6    0       4     5
19= 0    0    10     4     5
21= 5    6    10     0     0
26= 5    6    10     0     5

total
failed
students 5 + 6 + 10 + 4  + 5   = 30


Therefore, the maxium number of failed students is 30. So at least 100 - 30 = 70 students pass the exam.


But just in this case, the maximum number of failed students ncould be 30. If the distribution of failed question changes, it is possible the maximum number clouldn't reach 30.







Post by huck
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: oldwolf    时间: 2004-11-18 12:45
标题: The answer is 70
Here is why it should be 70.


The total wrong answers is

9+15+19+21+26 = 90

The maximum number of studnets who failed 3 questions could be 90 / 3 = 30

In this case, it is possible that 30 students failed the exam. The following is how the distribution of wrong answers are.


wrong
answers

9 =     5    0    0       4     0
15= 0    6    0       4     5
19= 0    0    10     4     5
21= 5    6    10     0     0
26= 5    6    10     0     5

total
failed
students 5 + 6 + 10 + 4  + 5   = 30


Therefore, the maxium number of failed students is 30. So at least 100 - 30 = 70 students pass the exam.


But just in this case, the maximum number of failed students ncould be 30. If the distribution of failed question changes, it is possible the maximum number clouldn't reach 30.







Post by huck
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: oldwolf    时间: 2004-11-18 12:45
标题: The answer is 70
Here is why it should be 70.


The total wrong answers is

9+15+19+21+26 = 90

The maximum number of studnets who failed 3 questions could be 90 / 3 = 30

In this case, it is possible that 30 students failed the exam. The following is how the distribution of wrong answers are.


wrong
answers

9 =      5    0    0       4     0
15= 0    6    0       4     5
19= 0    0    10     4     5
21= 5    6    10     0     0
26= 5    6    10     0     5

total
failed
students 5 + 6 + 10 + 4  + 5   = 30


Therefore, the maxium number of failed students is 30. So at least 100 - 30 = 70 students pass the exam.


But just in this case, the maximum number of failed students ncould be 30. If the distribution of failed question changes, it is possible the maximum number clouldn't reach 30.







Post by huck
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: oldwolf    时间: 2004-11-18 12:47
标题: The answer is 70
Here is why it should be 70.


The total wrong answers is

9+15+19+21+26 = 90

The maximum number of studnets who failed 3 questions could be 90 / 3 = 30

In this case, it is possible that 30 students failed the exam. The following is how the distribution of wrong answers are.


wrong
answers

9 =           5    0    0       4     0
15=          0    6    0       4     5
19=          0    0    10     4     5
21=          5    6    10     0     0
26=          5    6    10     0     5

total
failed
students  5 + 6 + 10 + 4  + 5   = 30


Therefore, the maxium number of failed students is 30. So at least 100 - 30 = 70 students pass the exam.


But just in this case, the maximum number of failed students ncould be 30. If the distribution of failed question changes, it is possible the maximum number clouldn't reach 30.







Post by huck
No, this is definitely not a question for computer algorithm. It is such a simple question that a smart brain needs only one flash to solve. I dont understand why an algorithm is needed while any kids knowing division could give the answer.
BTW, I could figure out the answer in a few seconds but dont understand the basis of sorting in your answer? It is funny!
作者: GiganticBalls    时间: 2004-11-18 12:52
HI:cool:

五年一班GiganticBalls同学应老师要求在黑板上演示解题思路，全班小朋友都听懂了，老师奖励一朵小红花。

OldWolf 同学的讲解从Sorting步骤开始就有很多小朋友听不懂了，老师奖励他八朵小红花，因为他具备了高等教育的计算机背景。
作者: berriuqam    时间: 2004-11-18 13:29
标题: 说实在的,这道题我也不懂答案
GiganticBalls的回答我开始觉得有道理,可是现在又觉得有点不对,但是哪里错了我也说不出.
请高人继续努力.另外为了方便理解建议用中文,毕竟是小学五年级嘛
作者: oldwolf    时间: 2004-11-18 13:40
标题: The right answer is 70.
GiganticBalls's answer is wrong, same as my previous wrong answer.

The right answer is 70. See the two messages before.

The idea is

The total wrong answer is 90. The maximum students who failed 3 questions is 90/3 = 30. In this case, it is possible 30 students failed 3 questions by each one. The other passed 70 students answered all 5 quesitons correctly and got a grade of 100. This is the at least number as all passed students got a grage of 100.


The distribution of wrong answers is listed in my previous meassage.


Sorry I can only read, can't write Chinese in my computer.

oldwolf

Post by berriuqam
GiganticBalls的回答我开始觉得有道理,可是现在又觉得有点不对,但是哪里错了我也说不出.
请高人继续努力.另外为了方便理解建议用中文,毕竟是小学五年级嘛
作者: berriuqam    时间: 2004-11-18 13:46
Post by oldwolf
GiganticBalls's answer is wrong, same as my previous wrong answer.

The right answer is 70. See the two messages before.

The idea is

The total wrong answer is 90. The maximum students who failed 3 questions is 90/3 = 30. In this case, it is possible 30 students failed 3 questions by each one. The other passed 70 students answered all 5 quesitons correctly and got a grade of 100. This is the at least number as all passed students got a grage of 100.


The distribution of wrong answers is listed in my previous meassage.


Sorry I can only read, can't write Chinese in my computer.

oldwolf
有一个问题我不理解,假如我把题目改一下：
第一题99人及格
第二题99人及格
第三题99人及格
第四题99人及格
第五题46人及格
要用你上面的算法：
（1+1+1+1+56）/3=20
最多有20人不及格......好像不对吧.
作者: oldwolf    时间: 2004-11-18 14:08
标题: Explaination
To Berriuqam:

Just in this case, the answer is 100-30 = 70. 30 is the maximum number of students who might fail the example, but this doesn't mean in every case the maximum number could  reach 30.

In your original question, the possible distribution of wrong answers could be

9 =  5 0 0 4 0
15= 0 6 0 4 5
19= 0 0 10 4 5
21= 5 6 10 0 0
26= 5 6 10 0 5

total
failed
students 5 + 6 + 10 + 4 + 5 = 30


Give you an example. The totaled failed questions are still 90, but
the first qestion only one answered wrongly, second 2, third 3, fourth 4, fifth 80. The maximum failed students can only be 5. The distribution is


Ques
wron
1    1       0     0     0     0    0
2    0       1      1     0     0   0
3    0        0     1     1     1   0
4     1       1     0     1     1   0
80    1      1     1     1      1  75


In this case, there are total 90 wrong answers, the maximum failed students are only 5.



Post by berriuqam
有一个问题我不理解,假如我把题目改一下：
第一题99人及格
第二题99人及格
第三题99人及格
第四题99人及格
第五题46人及格
要用你上面的算法：
（1+1+1+1+56）/3=20
最多有20人不及格......好像不对吧.

For this case, the possible maximum cloud be 20, but whether the maximum can reach 20 depends on the distribution of the wrong answers. Of course, for the distribution you gave, the maximum couldn't reach 20.

Hopefully the answer satisfy you.


Oldwolf
作者: berriuqam    时间: 2004-11-18 14:23
oldwolf,你的答案应该是正确的,只是方法对小学生来说难了一点

请大家再接再厉,有没有简单易懂的方法.
作者: 天秤座    时间: 2004-11-18 16:00
标题: Look At This Result: At Least 72 Passed!!!!
I would like to say that: Oldwolf didn't provide a clear algorithm, in stead, GiganticBalls has provided a good analysis. Only the result needs some correction. The following is the answer:
   
    at most: 9 students failed all 5 questions ( GiganticBalls is right at this stage).
   
    ===============Pay attention here================
   
    AT MOST: 19 students failed 4 questions. calculation is:
    9 failed: Q1+Q2+Q4+Q5;
    10 failed: Q1+Q3+Q4+Q5;
    0 failed all 5 questions.
   
    AT MOST: 28 students failed 3 questions. calculation is:
    19 faild: Q1+Q4+Q5;
    7 failed: Q2+Q3+Q5;
    2 failed: Q2+Q3+Q4;
    0 failed 4 or more questions.
   
    Therefore:
   
    不及格的最多有19+7+2=28人，
     则及格的最少有100-28=72人。
    ===============================
   
   
Post by GiganticBalls
HI:cool:
   
    没答对第一题的有100-81=19
    没答对第二题的有100-91=9
    没答对第三题的有100-85=15
    没答对第四题的有100-79=21
    没答对第五题的有100-74=26
    五题全错最多有9个人；
     
    去掉这9个人----
    没答对第一题的有19-9=10
    没答对第三题的有15-9=6
    没答对第四题的有21-9=12
    没答对第五题的有26-9=17
    四题全错的最多有6个人；
     
    去掉这9+6=15人----
    没答对第一题的有19-15=4
    没答对第四题的有21-15=6
    没答对第五题的有26-15=11
    三题全错的最多有4个人；
     
    不及格的最多有9+6+4=19人，
    则及格的最少有100-19=81人。
作者: 宝贝小猪    时间: 2004-11-18 16:26
hehe

你们算的太麻烦,同时错题人数为5,4,3,2,1的最大可能为

9
15
19
21
26


同时错3题的最大可能为19,故,至少100-19=81人及格
70人?差太多了,且算法混乱:eek:
作者: todaytoday    时间: 2004-11-18 16:30
标题: ONLY 天秤座 has the correct answer: 72
天秤座 has the correct answer: 72.  DING! DING!! DING!!!

Post by 天秤座
I would like to say that: Oldwolf didn't provide a clear algorithm, in stead, GiganticBalls has provided a good analysis. Only the result needs some correction. The following is the answer:
     
     at most: 9 students failed all 5 questions ( GiganticBalls is right at this stage).
     
     ===============Pay attention here================
   
     AT MOST: 19 students failed 4 questions. calculation is:
     9 failed: Q1+Q2+Q4+Q5;
     10 failed: Q1+Q3+Q4+Q5;
     0 failed all 5 questions.
     
     AT MOST: 28 students failed 3 questions. calculation is:
     19 faild: Q1+Q4+Q5;
     7 failed: Q2+Q3+Q5;
     2 failed: Q2+Q3+Q4;
     0 failed 4 or more questions.
     
     Therefore:
     
     不及格的最多有19+7+2=28人，
      则及格的最少有100-28=72人。
     ===============================
     
作者: oldwolf    时间: 2004-11-18 16:39
标题: ~, how can I explain it.
How come, I alreay provide you a distribution showing that there is a possibility that 30 students may fail the example. How can you say at most 28 students may fail. If you look at the distribution of wrong answers among students, you will get the conclusion:

Look at this situation: 100 students, 70 answered all 5 questions correctly. The other 30 failed 3 questions each one. Here is how they failed:

5 failed Question 2, 4, 5
6 failed Question 3, 4, 5
10 failed Question 1,4,5
4 failed Quesiton 2, 3, 1
5 failed Question 3, 1, 5

Total failed students 5+6+10+4+5 = 30

Total students failed Question 1: 10+4+5 = 19
Total students failed Question 2: 5+4 = 9
Total students failed Question 3: 6+4+5 = 15
Total students failed Question 4: 5+6+10 = 21
Total students failed Question 5: 5+6+10+5 = 26

For the above situlation, please count how many students failed the exam. It is 30?


9 = 5 0 0 4 0            Question 2
15= 0 6 0 4 5           Question 3
19= 0 0 10 4 5         Question 1
21= 5 6 10 0 0         Question 4
26= 5 6 10 0 5         Question 5

total
failed
students 5 + 6 + 10 + 4 + 5 = 30






Post by 天秤座
I would like to say that: Oldwolf didn't provide a clear algorithm, in stead, GiganticBalls has provided a good analysis. Only the result needs some correction. The following is the answer:

at most: 9 students failed all 5 questions ( GiganticBalls is right at this stage).

===============Pay attention here================

AT MOST: 19 students failed 4 questions. calculation is:
9 failed: Q1+Q2+Q4+Q5;
10 failed: Q1+Q3+Q4+Q5;
0 failed all 5 questions.

AT MOST: 28 students failed 3 questions. calculation is:
19 faild: Q1+Q4+Q5;
7 failed: Q2+Q3+Q5;
2 failed: Q2+Q3+Q4;
0 failed 4 or more questions.

Therefore:

不及格的最多有19+7+2=28人，
则及格的最少有100-28=72人。
===============================
作者: 天秤座    时间: 2004-11-18 16:45
标题: 现用中文post结果: 72
最多9人错5道。
最多19人错4道 (9人错1，2，4，5题； 10人错1，3，4，5题)。
最多28人错3道(19人错1，4，5题； 7人错2，3，5题； 2人 错2，3，4题)。

所以:
不及格的最多有19+7+2=28人，
      则及格的最少有100-28=72人。

Post by 天秤座
I would like to say that: Oldwolf didn't provide a clear algorithm, in stead, GiganticBalls has provided a good analysis. Only the result needs some correction. The following is the answer:
     
     at most: 9 students failed all 5 questions ( GiganticBalls is right at this stage).
     
     ===============Pay attention here================
   
     AT MOST: 19 students failed 4 questions. calculation is:
     9 failed: Q1+Q2+Q4+Q5;
     10 failed: Q1+Q3+Q4+Q5;
     0 failed all 5 questions.
     
     AT MOST: 28 students failed 3 questions. calculation is:
     19 faild: Q1+Q4+Q5;
     7 failed: Q2+Q3+Q5;
     2 failed: Q2+Q3+Q4;
     0 failed 4 or more questions.
     
     Therefore:
     
     不及格的最多有19+7+2=28人，
      则及格的最少有100-28=72人。
     ===============================
     
作者: oldwolf    时间: 2004-11-18 16:48
标题: ~~~~~~
天秤座, Just do me a favour, count the number of my previous message. Tell me the truth.:rolleyes:

Post by 天秤座
最多9人错5道。
最多19人错4道 (9人错1，2，4，5题； 10人错1，3，4，5题)。
最多28人错3道(19人错1，4，5题； 7人错2，3，5题； 2人 错2，3，4题)。

所以:
不及格的最多有19+7+2=28人，
则及格的最少有100-28=72人。
作者: eihpos    时间: 2004-11-18 16:51
干吗不列方程?有AK还用弓箭吗?:confused: :confused: :confused: :confused:
作者: oldwolf    时间: 2004-11-18 16:52
标题: Please look at my example, and count it.
Before post your intelligent method, please look at the following  situation. Tell me how many students failed the exam. :confused:

Look at this situation: 100 students, 70 answered all 5 questions correctly. The other 30 failed 3 questions each one. Here is how they failed:

5 failed Question 2, 4, 5
6 failed Question 3, 4, 5
10 failed Question 1,4,5
4 failed Quesiton 2, 3, 1
5 failed Question 3, 1, 5

Total failed students 5+6+10+4+5 = 30

Total students failed Question 1: 10+4+5 = 19
Total students failed Question 2: 5+4 = 9
Total students failed Question 3: 6+4+5 = 15
Total students failed Question 4: 5+6+10 = 21
Total students failed Question 5: 5+6+10+5 = 26

For the above situlation, please count how many students failed the exam. It is 30?
作者: oldwolf    时间: 2004-11-18 16:57

I do have a equation, list the numbers just for someone to understand. To prove my answer is right.

Equation is a little bit difficult to understand.

Post by eihpos
干吗不列方程?有AK还用弓箭吗?:confused: :confused: :confused: :confused:
作者: 天秤座    时间: 2004-11-18 17:37
标题: You are right. It's 70 rather than 72.
Thanks, you are right.  It's 70 rather than 72.

It is almost not possible to get this result without solving a set of equations. That is why I did a quick estimate, it seems not a correct one.

Post by oldwolf
  
I do have a equation, list the numbers just for someone to understand. To prove my answer is right.
  
Equation is a little bit difficult to understand.
作者: 木又子    时间: 2004-11-18 20:26
标题: 参考答案在此.
起用了多台高性能计算机:


http://my.cnd.org/modules/newbb/viewtopic.php?topic_id=32280&forum=1
作者: berriuqam    时间: 2004-11-18 20:56
呵呵,喜欢做思维体操的人还不少.再来一题,还是老规矩,不准列方程,不准编程,不准.......,用小学算术水平解题.


1000米长的距离，甲在一端，乙、丙在另一端相向而行，甲、乙、丙的速度分别是4公里/小时、6公里/小时、10公里/小时，丙在行进中，遇到甲就折返，遇到乙也折返，直到甲乙相遇。问丙和甲共相遇几次？和乙相遇几次？
作者: eihpos    时间: 2004-11-18 21:43
标题: 哲别,原名只儿豁阿歹,蒙古帝国神箭手,军事家,军事统帅
干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!:confused: :confused: :confused: :confused: :confused: :confused: :confused:
作者: berriuqam    时间: 2004-11-18 21:56
Post by eihpos
干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!干吗不让列方程不让编程?有AK还用弓箭吗?你以为你是只儿豁阿歹呀!:confused: :confused: :confused: :confused: :confused: :confused: :confused:
老兄,美国兵都高科技武装到牙齿了,不是还照样要练立正齐步走吗?
作者: oldwolf    时间: 2004-11-18 22:56
标题: General solution
Now everyone should agree the right answer is 70.

This is a general solution:

The at-least number of studnets who passed at least 3 questions

100 -(90/3) = 70.  70 is the least. For some wrong answer distributions, the minum cann't reach 70. But for the given dirstribution in this question, the minimum can reach 70.

The at-least number of students who passed at least 4 questions:

100 - (90/2) = 55. The result doesn't depend on wrong answer distribution.

The at-least number of students who passed 5 quesitons:
100 - (90/1) = 10. The result doesn't depend on wrong answer distribution.

The ..... 2... questions:

100 - (90/4) = 100 - 22 = 78. 78 is for ideal wrong answer distribution. For the given distribution in the quesiton, it is 100 - 21 = 79.


The .... 1... questions:

100 - (90/5) = 84. 84 is for the ideal distribution. That is when every question got the equal number of wrong answers. For the given distribution in the question, the answer is 100 - 9 = 91


Hope everybody have FUN.

Oldwolf
作者: jiang_mdong    时间: 2004-11-18 23:23
标题: 俺来解一下
俺来解一下， 解的不对请不要笑。

有下面几种可能及格
（答对的题目/最多的人数）
1 2 3 / 81
1 2 4/ 79
1 2 5/ 74
1 3 4/ 79
1 3 5/ 74
1 4 5/ 74
2 3 4/ 79
2 3 5/ 74
3 4 5/ 74
so the answer is 81
作者: ciel noir    时间: 2004-11-19 13:10
标题: 以题会友
也凑热闹，另拿一题来。
有一个六位数，我们用abcdef表示，分别与1、2、3、4、5、6相乘，得到六个新的六位数，这六个新的六位数，都是由a、b、c、d、e、f这六个数字组合而成。请找出abcdef。
作者: NorthFace    时间: 2004-11-19 22:47
标题: 70
Definition: MANPROBLEM: the fact of one problem being looked at by one test taker and possibly be solved by him (her). let's state that all problems are seen by all test takers and have a chance of being solved by each test taker.
SOLVED MANPROBLEM: the fact of one problem being worked on by a test taker and actually being solved by this person.

Total number of manproblem : 100 * 5 = 500
Total solved manproblem: 81 + 91 + 85 + 79 +74 = 410

Passing mark: n = 3
Lemma of Homogeneity: the least number of passing test taker happens when all the passing persons get all the problems correct and all the failing ones get exactly n-1 problems correct.

Proof: trivial.

Accoring to the lemma, in the case of least persons passing, everyone get at least 2 problems correct, which represent 100 * 2 = 200 solved manproblems. the remaining 410 - 200 = 210 solved  manproblems should be distributed to the passing persons by 3 solved manproblems each. so 210 / 3 = 70 is the least number of passing test taker.


finally, thanks to oldwolf for posting the question.
作者: NorthFace    时间: 2004-11-19 23:07
标题: Sorry it's berryquam who posted the question.
to oldwolf: there is no problem to distribute 60 solved manproblems to 30 failing persons with exactly 2 manproblems each person (or you can we need to distribute 90 unsolved manproblems to 30 failing persons with exactly 3 each person.)

now the interesting question is THERE ARE TOTALLY HOW MANY DIFFERENT DISTRIBUTIONS?
作者: henry514    时间: 2004-11-20 11:10
每天就是学会计，很少做这么复杂的题啦！
作者: Michael_huang    时间: 2004-11-20 18:06
答案：abcdef=142857


Post by ciel noir
也凑热闹，另拿一题来。
有一个六位数，我们用abcdef表示，分别与1、2、3、4、5、6相乘，得到六个新的六位数，这六个新的六位数，都是由a、b、c、d、e、f这六个数字组合而成。请找出abcdef。
作者: soloman    时间: 2004-11-20 21:19
26
21+9
15+19
the maxium number of students who have 3 wrong question is 26
so the minium number of students passed is 74
作者: Joe_xj    时间: 2004-11-20 21:49
标题: 答案是70。
1。我并没做出来。看了别的网站的解题步骤，想明白的。（这里有位兄弟也做对了，但他是用英文解释的。我英语差点，不能FOLLOW）
2。答案为81的以GiganticBalls为代表，错误在于认为不及格的人里面一定有人多于三题不对。这是与‘至少’的要求相违的，换句话说就是人为减少了不及格的人分布的可能性，比如所有不及格的人都仅有三题不对。
作者: GiganticBalls    时间: 2004-11-21 00:26
HI:cool:

确实有道理，不过小红花就不要退还了吧。
Michael Huang的解题方法是什么？
作者: 白石桥的小楼    时间: 2004-11-21 01:20
提示: 作者被禁止或删除 内容自动屏蔽
作者: GiganticBalls    时间: 2004-11-21 14:15
HI:cool:
Post by 白石桥的小楼
总的错题数是 (100-81)+(100-91)+(100-85)+(100-79)+(100-74)=90

因为错3道以上就不及格了.
那么假设每个人都是错3道,那么90道错题被30个学生充分分配.也就是说最多的不及格的学生是30人.
因此至少有70人及格!
北京的孩子果然灵巧．
作者: ciel noir    时间: 2004-11-22 21:41
Post by Michael_huang
答案：abcdef=142857

结果对，请问用什么方法做的？谢谢！
作者: berriuqam    时间: 2004-11-23 00:10
有一个六位数，我们用abcdef表示，分别与1、2、3、4、5、6相乘，得到六个新的六位数，这六个新的六位数，都是由a、b、c、d、e、f这六个数字组合而成。请找出abcdef。 abcdef=142857
我用了最笨的办法对不起,这个帖子贴出来表格就是没法对齐)
**6 5 4 3 2 1
**************
2 *6 0 8 6 4 2

3 *8 5 2 9 6 3

4 *4 0 6 2 8 4

5 *0 5 0 5 0 5

6 *6 0 4 8 2 6

7 *2 5 8 1 4 7

8 *8 0 2 4 6 8

9 *4 5 6 7 8 9



(1).a=1这一点大概大家都没意见吧.
(2).现在确定最后一位数.这个数和1,2,3,4,5,6分别相乘的尾数必须是1(因为根据上一步,1已确认是其中的一个数字.根据已知的条件,必须尾数出现一次1).查上面的表,可以知道只有7符合条件,所以尾数是7.
(3).由尾数7推断倒数第二位数字:根据已知的条件,abcdef这个数和1,2,3,4,5,6分别相乘后的乘积的十位数必须有一次是1.因为7和1,2,3,4,5,6分别相乘的进位只能是4,3,2,1.所以,这个数必须和6相乘尾数是7,或和5相乘尾数是8,或和4,3相乘尾数是9,或和2相乘尾数是0.查上面的表,可以知道只有5符合条件,所以倒数第二位数字是5.
(4)由倒数第二位数字5推断倒数第三位数字:..........依此类推.

呵呵,这办法够笨吧.
作者: 天秤座    时间: 2004-11-23 10:32
标题: 事情不是那么简单吧
事情不是这么简单的吧。因为您的假设“每人错三题”不一定成立(这回是碰巧成立了)。



把题改成这样：44人做错第1题，43人做错第2题，1人做错第3题，1人做错第4题，1人做错第5题。总共还是90道错题，请您用您的法子算算至少几人及格？这回该是97人及格了吧。

Post by 白石桥的小楼
总的错题数是 (100-81)+(100-91)+(100-85)+(100-79)+(100-74)=90

因为错3道以上就不及格了.
那么假设每个人都是错3道,那么90道错题被30个学生充分分配.也就是说最多的不及格的学生是30人.
因此至少有70人及格!
作者: berriuqam    时间: 2004-11-23 12:20
对不起,表格打错了一个数字,应该是

**6 5 4 3 2 1
**************
2*2 0 8 6 4 2

3 *8 5 2 9 6 3

4 *4 0 6 2 8 4

5 *0 5 0 5 0 5

6 *6 0 4 8 2 6

7 *2 5 8 1 4 7

8 *8 0 2 4 6 8

9 *4 5 6 7 8 9

解题的关键是判断组成ABCDEF的数字在不同的6个位置各出现一次



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