2026希望杯国际数学邀请赛巅峰对决团队思考赛IHC4-TT四年级数学试题

Mathematics Invitational International Hope Cup 2026 Global Peak Challenge (IHC 4) 2026希望杯国际数学邀请赛巅峰对决(HC4) nternationa Team Thinking Round团队思考赛 There are 10 questions in total,each worth 10 points,for a total of 100 points Time limit:45 minutes. Discussion is allowed,each team answers one test paper,and only one answer sheet is submitted 共10道题，每题10分，共100分。 限时：45分钟。 允许讨论，每个队答一份试卷，只提交一份答题卡。 TT-1.For a sequence of distinct natural numbers,if the number on the left is greater than the number on the right (the two numbers may be adjacent or non-adjacent), the pair is called an inversion pair.The total number of inversion pairs in the sequence is called the inversion mmber of the sequence.For example,in the sequence 2,3,1,4,there are only two inversion pairs:(2,1)and (3,1),so the inversion mmber is 2.What is the inversion mmber of the following sequence? 对于由互不相同的自然数组成的数列，若左边的数大于右边的数（两数可相 邻，也可不相邻)，则称这一组数为一个逆序对：数列中全部逆序对的总数 量，称为该数列的逆序数。例如数列2,3,1,4，仅存在(2,1)、（3,1) 两个逆序对，逆序数等于2。那么以下数列的逆序数是多少？ 2、6、8、3、1、7、5 ational Hope Cup international Hope Cup International Hope Cup Mathematics Invitational TT-2.Lydia writes consecutive three-digit natural numbers starting from 226:226, 227,228,...,However,she misses writing one of the three-digit numbers.For each number she writes,she calculates the product of its digits,and then adds all of these products together.The final sum is exactly 2026.What is the three-digit number that Lydia missed? Lydia从226起依次书写连续三位自然数：226,227,228，…，但她漏写 了其中的一个三位数。她对写出的每个数计算各位数字的乘积，再将所有乘 积求和，计算结果恰好等于2026。那么Lydia漏写的三位数是多少？ TT-3.As shown in the figure,in the regular hexagon ABCDEF,the side lengths of the three smaller regular hexagons centered at G,H,and I are each half the side length of regular hexagon ABCDEF.Given that the area of triangle GHI is 254 square centimeters,what is the area of regular hexagon ABCDEF in square centimeters? 如图，在正六边形ABCDEF中，以G、H、I为中心的三个小正六边形边长 是正六边形ABCDEF边长的一半，已知三角形GHⅢ的面积是254平方厘米， 那么正六边形ABCDEF的面积是多少平方厘米？ ternational Hope Cup international Hope Cup International Hope Cup Mathematics Invitational TT-4.Andrew,Bonnie,Cindy,Derry,and Eric take a math exam and are ranked according to their scores.Ties are allowed.How many different ranking outcomes are possible?(For example,Andrew in first place with the other four students tied for second,and Bonnie in first place with the other four students tied for second,are regarded as two different ranking outcomes.) Andrew、Bonnie、Cindy、Dey、Eic五位同学参加一次数学考试，并按成 绩排名。排名允许出现同分并列。5人的排名结果共有多少种不同的情况？ (例如，Andrew第一名、其余四人并列第二名，与Boie第一名、其余四 人并列第二名，属于两种不同的排名结果。) TT-5.From the 2026 natural numbers 1,2,3,...2025,2026,what is the maximum number of numbers that can be selected such that the difference between any two selected numbers is not equal to 7? 从1,2,3，.，2025,2026这2026个自然数中，最多可以取出多少个数， 使得其中任意两数的差都不等于7？ TT-6.Using the digits 1,2,3,4,and 5,how many five-digit numbers with no repeated digits can be formed that are divisible by 24? 用数字1,2,3,4,5组成无重复数字的五位数，其中能被24整除的五位 数共有多少个？ International Hope Cup Mathematics Invitational TT-7.As shown in the figure,3 identical tokens are placed in the given grid area. Each square can contain at most one token,and any two squares containing tokens share neither a side nor a vertex.How many different possible airangements are there? 在如图所示的方格区域A~I内摆放3枚相同的棋子，每个方格最多放置一枚 棋子，任意两枚棋子所在方格既无公共边，也无公共顶点，一共有多少种不 同的摆放方案？ A B 6International Hot International Hope Cup TT-8.A seven-digit number is formed using only the digits 1 and 2.The number must contain both 1 and 2,and no two consecutive digits can both be 2.How many such seven-digit numbers are there? 只用数字1和2组成一个七位数，要求这个七位数中同时包含1和2，但 Hope 能出现连续的2，这样的七位数共有多少个？ nternational Hope Cup International Hope Cup 4 International Hope Cup Mathematics Invitational TT-9.Thirteen distinct non-zero natural numbers are placed into the 13 circles shown in the figure.The sum of the four numbers at the vertices of each square in the figure is required to be 26.What is the maximum possible value of the product of the three numbers marked Y.Y,and Z? 将13个互不相等的非零自然数分别填入下图的13个圆圈中，要求图中每一 个正方形四个顶点处的数相加的和均为26。那么图中标记为X、Y、Z的三 个数相乘的乘积最大是多少？ TT-10.There are 100 students standing in a line,numbered from 1 to 100 from left to right.Candies are distributed to each student.The distribution must satisfy the following condition:For any student p,there exists a student adjacent to P on either the left or the night,such that the total number of candies received by p and O is no less than P's number.What is the minimum total number of candies that must be distributed to the 100 students? 共100名学生排成一排，从左到右依次编号为1至100。给每名学生分发糖 果，要求对任意一名学生P,都能找到与P左或右相邻的一名学生Q,使P、 ?两人糖果数量之和不小于P的编号。那么至少要给这100名学生分发多少 枚糖果？ hational Hope Cup International Hope Cup International Hope Cup Mathematics Invitational Answer (答案) Question 题目 TT-1 TT-2 TT-3 TT-4 TT-5 TT-6 TT-7 TT-8 TT-9 TT-10 Answer 答案 10 241 2032 541 1015 10 8 33 72 1717 International Hope Cup International Hope Cup Hope Cup International Hope Cup International Hope C nternational Hope Cup International Hope Cup Internatio