puzzleup 2018

solomon_007 · 发表于 2018-10-21 22:41

lugionline 发表于 2018-10-21 20:34

Niubility！
前面听你科普过，好像又是什么马尔科夫链的东东。。。

newkid · 发表于 2018-10-22 21:33

lugionline 发表于 2018-10-21 20:34

这个公式是如何得到的? 其他编号的概率要怎么算?

solomon_007 · 发表于 2018-10-23 09:43

lugionline 发表于 2018-10-21 20:34

对啊，大神，给我们讲讲，公式一步一步怎么来的啊？

newkid · 发表于 2018-10-24 22:18

#13 FAMILY TEAMS

Four families, each with four members (mother, father, daughter and son) apply to attend a competition. Three teams of three people will be selected. Each team will have exactly one mother, one father and one child (daughter or son) and none of the members will be from the same family.

How many different ways the teams can be formed? (Two formations are considered the same if team memberships are the same but team orders are different.)

四个家庭，每个家庭有四名成员（母亲，父亲，女儿和儿子）申请参加一个比赛。有三个三人团队会被选出。每个团队恰好有一个母亲，一个父亲和一个孩子（女儿或儿子），并且所有成员都不会来自同一个家庭。

总共有多少种组成团队的不同方式？（如果团队成员相同但顺序不同，则两种方式被认为是相同的。）
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这个用SQL是很容易模拟出来的。

solomon_007 · 发表于 2018-10-25 00:14

13 #

这题太容易了。。。

SQL> with t as (select 'M' a,'F' b,'S' c,'D' d from dual),
  2    r as (select level n from dual connect by level <=4),
  3    s as (select rownum rn,a||n a,b||n b,c||n c,d||n d from t,r),
  4    f as ( select s1.a,s2.b,s3.c
  5             from s s1,s s2,s s3
  6             where s1.rn <> s2.rn
  7                and s2.rn <> s3.rn
  8                and s1.rn <> s3.rn
  9             union all
10             select s1.a,s2.b,s3.d
11             from s s1,s s2,s s3
12             where s1.rn <> s2.rn
13                and s2.rn <> s3.rn
14                and s1.rn <> s3.rn )
15  select
16       --f1.a a1,f1.b b1,f1.c c1,f2.a a2,f2.b b2,f2.c c2,f3.a a3,f3.b b3,f3.c c3
17       count(*)
18 from f f1,f f2,f f3
19 where f1.a <> f2.a
20    and f2.a <> f3.a
21    and f1.a <> f3.a
22    and f1.b <> f2.b
23    and f2.b <> f3.b
24    and f1.b <> f3.b
25    and f1.c <> f2.c
26    and f2.c <> f3.c
27    and f1.c <> f3.c
28  /
  COUNT(*)
----------
   12480