puzzleup 2016

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五个数字
从1到100( 1，2，…、99、100)之间随机选择五个数字。 如果所选的数字都不同，且其和等于100，则把其中最小的数记下来。如果把这个过程重复多次，上述记下来的数字的平均值将是多少？
注意：所有数字都有同样的选择概率。用作为一个化简的分数输入你的答案。 例如:12/23

No: 16       November 09, 2016  





FIVE NUMBERS

Five numbers are selected randomly between 1 and 100 (1, 2, ..., 99, 100). If the selected numbers are all different and their sum is equal to 100, the smallest number is noted. If this process is repeated many times, what would be the average of the noted numbers?

Note: All numbers have the same probability of selection.

Enter your answer as a simplified fraction. Example:12/23

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不知道是否放回抽样

newkid

每个都不相同，当然是不放回了。这个用 sql 很容易的吧。现在我上不了 itpub, 手机没问题，真是奇怪。

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No: 17       November 16, 2016  



SEVEN

SEVEN

There is a number with digits appearing at most twice and all the numbers formed by adjacent two digits are divisible by 7.

What can be the maximum value for this number?

Example:63563 is such a number (63, 35, 56 and 63 are divisible by 7) but it is not the maximum.

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17题
7
一个数各位相同数字最多出现2次，并且相邻数字组成的数都能被7整除，求这样的最大数。

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with t as(select (level+1)*7 l from dual connect by (level+1)*7<100),
a as(select power(2,level-1)b,floor((level-1)/2) a from dual connect by level<=20)
,t1(lv,sb,sa)as(
select 1,b,a from a
union all
select lv+1,sb+b,sa*10+a from t1,a
where bitand(b,sb)=0
and mod(mod(sa,10)*10+a,7)=0)
select max(sa) from t1;

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不知道00、07算不算被7整除

newkid

〇〇 发表于 2016-11-16 20:41
不知道00、07算不算被7整除

当然算了。没什么难度的题。

WITH t (num) AS (
SELECT CAST(LEVEL AS VARCHAR2(30)) FROM DUAL WHERE LEVEL>=10 AND MOD(LEVEL,7)=0 CONNECT BY LEVEL<100
UNION ALL
SELECT t.num||n FROM t,(SELECT LEVEL-1 n FROM DUAL CONNECT BY LEVEL<=10)
WHERE REGEXP_COUNT(t.num,n)<2
      AND MOD(SUBSTR(t.num,-1)||n,7)=0
)
SELECT * FROM t ORDER BY TO_NUMBER(num);

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我就喜欢没难度的，用regexp_count求重复次数，不错

lugionline

Out[6]= 98498421

每人做前面的题? 看来Oracle 是没落了