oldwolf

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!

GiganticBalls

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。

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

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

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

berriuqam

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.

oldwolf

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

berriuqam

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.

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。
    ===============================
   
   

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。

宝贝小猪

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:

todaytoday

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。
     ===============================