新模考数学题-求助

tiwwang

以下是引用hitlzc在2005-12-27 7:55:00的发言：

我觉得这个解释比较合理：

If n=2m, then h(n)=2^m*m!

Since the first term includes m!, all natural numbers from 2 to m would be a factor of h(n)=h(2m) and would not be a factor of h(n)+1. In other words any factor that h(n)+1 would have would be greater than m. （也就是说必然因子比m大）

In this case h(100)+1=2^50*50!+1, so the least prime factor would be greater than 50. So I would choose 5.

这句话有点不懂 ，为什么由这个式子可以推出最小的质因子大于50啊

hitlzc

就是因为这个呀：Since the first term includes m!, all natural numbers from 2 to m would be a factor of h(n)=h(2m) and would not be a factor of h(n)+1. In other words any factor that h(n)+1 would have would be greater than m. （也就是说必然因子比m大）

所以：In this case h(100)+1=2^50*50!+1, so the least prime factor would be greater than 50

maple_leaf

第一题

for every positive even integer n, the fonction h(n) is defined to be the product of all the even integers from 2 to n, inclusive.

So we could write the following:
h(2)=2=2*1
h(4)=2*4=(2*1)*(2*2)=2^2*(1*2)
h(6)=2*4*6=(2*1)*(2*2)*(2*3)=2^3*(1*2*3)
h(8)=2*4*6*8=(2*1)*(2*2)*(2*3)*(2*4)=2^4*(1*2*3*4)
...
You can see if n=2m then
h(n)=2^m*(1*2*...*m)=2^m*m!

This is exactly what you need ot know to solve the problem.
At a minimum the smallest prime factor is 53.

For any factorial + 1 the smallest factor (apart from 1) is greater then any of the members of the factorial

2! + 1 = 3: smallest factor is 3
3! + 1 = 7: smallest factor is 7
4! + 1 = 25: smallest factor is 5
5! + 1 = 121: smallest factor is 11

根据这两个帖子，可以得到答案应该大于50，因此选最后一个了？谁能知道到底最小的质因数是什么呢？

另，中数是一个数列从大到小或从小到大的排序中间的数吗？我以为只是从小到大。

maple_leaf

第三道排列组合题，还有个条件呢，two seating arrangments are considered differently only when the positions of the people are different relative to each other. 难道不用考虑吗？大家再发动脑筋，牛牛们看过来啊！

还有第二道，怎么得出1答案的呢？

赫连勃勃

以下是引用maple_leaf在2005-12-27 11:33:00的发言：

第三道排列组合题，还有个条件呢，two seating arrangments are considered differently only when the positions of the people are different relative to each other. 难道不用考虑吗？大家再发动脑筋，牛牛们看过来啊！

还有第二道，怎么得出1答案的呢？

这个条件很重要，也就是说先排列P55,然后根据这个条件除以5

赫连勃勃

问题2里面的III的确不对，前七项都可以是median13000

maple_leaf

以下是引用赫连勃勃在2005-12-27 11:53:00的发言：

这个条件很重要，也就是说先排列P55,然后根据这个条件除以5

为什么要除5啊,还是不明白,偶弱啊,请详细讲讲.

那第二题的答案1是怎么求出来的?

赫连勃勃

以下是引用maple_leaf在2005-12-27 18:07:00的发言：

为什么要除5啊,还是不明白,偶弱啊,请详细讲讲.

那第二题的答案1是怎么求出来的?

五个人坐一圈，考虑是否是不同分配的时候只考虑相互位置不考虑每个人实际坐哪个位置。比如

    1

2        5

  3   4

和

    5

1       4

   2  3

算作一种分配。

maple_leaf

哦,明白了,谢谢大家

期待蔚蓝

谁能再给解释一下这道题目啊？

Last month 15 homes were sold in town x, the average sale price of the homes was $150000 and the median sale price was $130000, which of the following statement must be true.

1) at least one of the homes was sold for more than $165000

2) at least one of the homes was sold for more than $130000 and less than $150000

3) at least one of the homes was sold for less than $130000.

答 （1）