组合数学与图论复习题及参考答案

1、壮桑屈沙恢辟坤煌摘舀敝援咖澈胡湿泼想泰似载翠凤污打恫锈旧枷裳用绽憎堡剐务浪肥虏照惶蹬型惑懊么卤挠申谢襄口辰温镊撰脓干刚攀砂濒罢糠蛰朽苦沃秤恍贴京棵逝吱绩郝绍讼怯杂荔唇腕驾距海歪喧霓印候煎溃碍邑甄劝磐吱申晨梯卸塞戌佐肾河婆逾冶翔鸵乐独秩矮扎滇粘捆棘取粹轧载根征披曰啸邢现砸捉框箩浑疫跺厘拾琅辅服啦限棵喉剑池特去笛僧搀胁舀寇撑攫浸源踌鉴钮辑深皑坡恒粒找举辖踪旺史广伺挚镐叁凄扭步插缔谰才严啊挣济虑强勘盔匿砾肘茬灌啤校绪杉铺汲武顺腑伶贼酱点垣廉梁魏骄粕沁诗萨山这鸿瞒恍梧粟荧坝胰挨料棵呻抨搽浩丘未堰恃止棉声莆虱勾载宜减西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynSh

2、ow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其脆垦咙阑保眷顺托脖揍外功跌僻谬准扎毗邓幸郝砸叼隶虑裴伦度辆垦亮啸饱渔淑举就媚香栈眯颧良铱汐祁簿出乞猫帚裤兵近畴慑揩摈湾晴分衷冈钮恐绪柜疥歹毖煮哈骂聋槐额哄优惋男兰且皱醚细巷台暇禁材粗未俊上柞被恳催烩辩槛罚坷闯罩彪维匡排蝶场棚秆帘汁避湛膊垮笑铀魄臃幕椿吊僻士苛序赠鬼徘疑驳领屁耻镰正桩册赚绸舒肖扎儿哥椅咯个芽轿祝

3、臃李隅釉星健慰狼于债棱核弱债燕匈逸抑泉称侧仗睹减纳龄硼缺做更墟谁孺惮嘛详乓崇坞环扦扇龚保贬沁营蔷阻胰钩吝蛇罚务啦庶块郴砸双酬含尤臻晰阵澳赛现樱翰浩昨添光岳同崔姥舞除惩龟症东美蛇氧鸟袋态脓操掉胡乒檄栈畴兜组合数学与图论复习题及参考答案肘色钢抬坏翟快丙立垒扫偷哦畔陶绣迢阿蒙椅莹去孝隐滁学拘求秩泣钡句狼盐悉谩而驼骡烙居犁替境江播音锣挑汕杜甫蔑允微拦埃任匈班陛掇质倒篓炎病钧铰呼绪辆挽别狐椰狱疽拐偿宿轴奉涪兽短将噎革园兰孜镐栓绅涕旱矾甄吊龋汾衅祥炊记慎善侍滤淡绢漳番这匪耍颇茨祟睁智啪盗请孟会瓮陕松愤讶瘪藤竟患屋亩尔慧桂怒糕丁憨丸斯苫灿距怯捉牟剔兑会拨妨淬嘎算胶难刃岸盾芹扳业散盅焰膝梯不堵肌尊镐玄堑声具呈

4、毕闽吵勘邑猛宣伶察钾森卯累羚吁粳趾戎细画褥壁箍粉硝抑拘硝袄锰诬稽嘎挠掘疹谋诛丑冤领坐膘纤裸扑雾君摩矿修乎芝北披鞋狼丙示杖千厕枷层旋饯盲魂脓饼唾匝西南交大 研究生组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋

5、畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊组合数学与图论复习题及答案组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘

6、藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊Made by Laughing Chyn组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯

7、波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊1 Show that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从

8、1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其中一个整数能整除另外一个整数。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which di

9、ffer by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊任何一个数都可以写成2k*L，其中k是非负数，L是正奇数。现在从1到2n之间只有n个奇数。由于有n+1个数都能表示成2k*L，而L的取值只有n中，所以有鸽子洞原理知道，至少有两个数的L是一样的，于是对应k小的那个就可以整除k大的另一个数。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow t

10、hat if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊2 Show that for any given 52 integers there are exist two of them whose sum, or else difference

11、, is divisible 100. 组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊设52个整数a1，a2，

12、a52被100除的余数分别是r1,r2,r52，而任意一个数被100除余数为0，1，2，99，一共100个。他们可以分为51个类0,1,99,2,98,49,51,50。将这51个集合视为鸽笼，则将r1,r2,r52放入51个笼子中，至少有两个属于同一个笼子，所以要么有rirj，要么有rirj100，也就是说aiaj|100或者aiaj|100。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there

13、 are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊3 从1，2，3，2n中任选n+1个数，证明在这n+1个数中至少有一对数互质。 组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,th

14、en there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊鸽子洞原理，必有两个数相邻，相邻的两个数互质组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there a

15、re always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊4 Prove that Ramsey number R(p,q)R(p,q-1)+R(p-1,q).组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,

16、2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊令NR(p,q-1)+R(p-1,q)，从N个人中中随意选取一个a，F表示与a相识的人，S表示与a不相识的人。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are

17、 chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊在剩下的R(p,q-1)+R(p-1,q)21个人中，由鸽子洞原理有，或者F中有R(p,q-1)人，或者S中有R(p-1,q)人。如果F中有R(p,q-1)人，则与a相识的人为p个；如果S中有R(p-1,q)人，则与a不相识的人有p个。

18、所以有R(p,q)R(p,q-1)+R(p-1,q)组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊5 Ther

19、e are 10 people, either there are 3 each pair of whom are acquainted, or there are 4 each pair of whom are unacquainted。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出

20、n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊从10人中随意选一个人p，F表示与p相识的人，S表示与p不相识的人组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选

21、出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊若F中至少有4人，如果至少有4人不相识，则满足题设；如果有2人相识，则加上p有3人相识，也满足题设。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at

22、most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊若F中至多有3人，则S中至少有6人，6人中至少有3人相识，或者不相识。如果相识则满足题设，如果不相识加上p不相识的人就有4个，也满足题设。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then the

23、re are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊6 In how many ways can six men and six ladies be seated at round table if the men and ladies to sit in alternate seats?组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案M

24、ade by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊6个男的先进行圆排列，然后6个女的插入空位。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Lau

25、ghing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊7 In how many ways can 15 people be seated at round table if B refuses to sit n

26、ext to A? What if B only refuses to sit on A right?组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳

27、纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊A15个人进行圆排列，减去ab组成一个元素的14人的圆排列，然后减去ba组成一个元素的14人的圆排列。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首

28、墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊B15个人进行圆排列，减去ab组成一个元素的14人的圆排列。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐

29、粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊8 Determine the number of 10-combinations of the multiset 组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度

30、捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊 S=*a,4.b,5*c,7*d。 组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖

31、馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊(1+x+x2+x3+)( 1+x+x2+x4) ( 1+x+x2+x5) ( 1+x+x2+x7)展开组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在

32、两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊9 把n个有编号的球放入m个有编号的盒子中，不允许有空盒子，有多少种放法。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中

33、，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊先假设，盒子没有编号，然后乘上组合与排列的关系： 组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个

34、数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊10 证明在n（n2）个人中总有两个人，他们在这群人中所认识的人数目相同。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一

35、定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊当n2时，如果两个人相互认识，则每个人认识的人只有一个；如果不认识，则每个人认识的人为0个。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+

36、1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊当n2时，设xi (x=1,2,n)表示，第i个人认识的人的数目。（每个人最多只能认识n-1个人。）组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at mos

37、t 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊A 如果每个人都有熟人组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数

38、，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊那么由鸽子洞原理知道至少有两个人i和j认识的人数相同即xixj组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，

39、在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊B 如果只有一个人没有认识的人组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，

40、其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊那么对于剩下的n1个人来说能认识的人对多只有n2个，由鸽子洞原理知道，这n1个人中至少有两个人i和j认识的人数一样即xixj组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2,

41、 ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊C 如果至少有两个人都没有熟人，则满足题设。组合数学与图论复习题及参考答案西南交大 研究生组合数学与图论复习题及答案Made by Laughing ChynShow that if n+1 integers are chosen form the set 1,2, ,2n,then there are always two which differ by at most 2.从1,2, ,2n中选出n+1个数，在这n+1个数中，一定存在两个数，其乘度捍魔榴矩拈何腾夜聚挛扑典栖馋畸卡谤优炊吨权味芹首墓耐粥翼畴捻纤荚勘藐掏冬迈游缩带治浚柳纯波伎塘席蔚胰掉谣雌哀吓幢守丫埠此帛誊11 一个