berriuqam

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?

oldwolf

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

jiang_mdong

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

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。

NorthFace

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.

NorthFace

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?

henry514

每天就是学会计，很少做这么复杂的题啦！

Michael_huang

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。

soloman

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

Joe_xj

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。