输血一狗狗，求此类题思路。。

Jessica0320

1，2，3，4，5 组合密码，问有多少种偶数不相邻？

狗狗里有，近日我实战也碰到了。。。排列组合，一向糊涂。。。

哪位高人指点一下思路？

肉圓兒

__1__3__5__ 三个奇数先放好
这时候一共有4个空可以插。。
所以是P33（3个奇数的顺序）乘以C2，4（偶数从4个空里选2个）乘以P22（3个偶数的顺序）
6乘6乘2=72

Jessica0320

事实上，我多写了个6。。。是1，2，3，4，5。。。我改一下，烦请您也改一下，省得咱误导大家哈。。

最最重要，肉圆儿同学，那思路是不是说，先看那三个奇数咋排，然后看放偶数的位子有多少种，然后位子定了，再看这几个偶数怎么个排法。。。

所以，应该是：P33 * C42* P22= 6*6*2= 72！ 哈哈！

明白了，谢谢肉圆儿同学哈！

肉圓兒

。。。我表示 我还得跟着改。。。不然人家说我是傻子- -

Jessica0320

难为您啦哈，哈哈。。。不好意思。。。偶实在糊涂。呵呵

肉圓兒

~~~~。。。别您。。我比你小么。。。

Jessica0320

说的是。。。您定比我小。。。不过，您是前辈，您辈儿大！嘿嘿。。。

sdcar2010

Another way is to calculate cases of 偶数相邻.

_1_3_5_  put a block of [24] or [42] into any of the 4 open space among three odd numbers.

3! * 2 * 4 = 48
5! = 120
120 - 48 = 72

efrenreyes

7楼还真是很喜欢回答问题啊……大晚上一上来又见到你

你既然已经选择了先求偶数相邻的思路，那不就是把[24] or [42]和1、3、5的排列，从1、2、3、4、5的排列中扣除吗，所以5！-4！*2！即可得答案。

如果真是就考这道原题，我也会选择逆推的方式，因为这样路径最简洁（心算时间不会超过10秒）；但是对于偶数超过2个的题目，就是肉圆的正推法最简洁了。

你在唯一用逆推更简洁的题设情况下，选择了一种比正推更复杂的表述方式。尤其是这个3! * 2 * 4，真的很让人怀疑你的兴趣，究竟是试图在题设下寻找最优美的解题路径以获得思考的快乐，还是仅限于罗列更多的解法（尽管可能远比之前已列出的繁赘而不可能被任何思维正常的人采用）以获取积分混个更高的论坛头衔…………

sdcar2010

One possible reason is that if I use less than 20 seconds to solve a question, I would run the risk of being accused of cheating during the GMAT test.

Another possible reason is that a lazy person such as me would like to use a known framework proposed by MeatCircleEr, as a matter of showing respect, for my own strategy and to show the similarity and difference between these two strategies.

Still another possible reason is that generally speaking, a diagram showing the possible arrangement visually for viewers would help them understand the abstract meaning behind purely mathematical operations.

Still, still another possible reason is that I simply want to put out an imperfect answer in the hope that some smarty pants might gloatingly point it out.

Still, still, still another possible reason is that I assume everyone knows the meaning of a proverb called "Never look a gift horse in the mouth."

Still, still, still, still another possible reason is that the TITLE for the thread is asking for thinking processess rather than the quickest or the best solutions.

Still, still, still, still, still another possible reason is that contributing to discussion of an interesting question is much better than disparaging another person or his/her ideas.