1 . 设a,b,c,
,
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731fceab5fd883f0598f34713db4242f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e209cfb730513dc749d8efe85ca50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0e70c2e75fad4d49574103c7c5f03d.png)
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2 . 给定正整数n,
,记
从
的一一映射f称为是可
划分的:若X可划分为k个非空子集
,
,…,
,且
(
,2,…,k)(即
,且
,
,…,
两两的交集为空集,
).已知f是一个X的
划分的一一映射,
,
,…,
是1,2,…,n的一个排列,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7863f720c810be5158d84a0e9b5e5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056db510d3e75cc12adc855015ad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31556cfdfe2ebbf0dacfbb9e28f968ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307e85746fa628650484d89e3b9809ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd2781fa12b524b3b01f02d7b9d8f68a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88501f72db91e5cf1a42114b4300ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb67fb9b5a8e475087ecc2a0aaca869a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7187f7b32e990b39cf9df84428660a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307e85746fa628650484d89e3b9809ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04a8b7a7595251251b8e0b7e665e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5453ec6a9e8b96357c888ea863ddcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a10902a745902e85100175a0d7788fe.png)
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3 . 如图,
是
的内心,
的外角平分线交
于点
,直线
交
外接圆于点
,直线
与直线
交点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020059d62af7498039f091de6f005ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c845bb8ceaa4caef3af4f1e4366b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3e927b7b2383ccded03838ae8b30b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/f91571d9-b908-418b-9844-65875710ce74.png?resizew=220)
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4 . 定义:如果甲队赢了乙队,乙队赢了丙队,而丙队又赢了甲队,则称甲乙丙为一个“友好组”.
(1)如果19支球队参加单循环比赛,求友好组个数的最大值;
(2)如果20支球队参加单循环比赛,求友好组个数的最大值.
(1)如果19支球队参加单循环比赛,求友好组个数的最大值;
(2)如果20支球队参加单循环比赛,求友好组个数的最大值.
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