2026希望杯国际数学邀请赛巅峰对决个人思考赛IHC6-I四年级数学试题

International Hope Cup Mathematics Invitational 2026 Global Peak Challenge (IHC 6) 2026希望杯国际数学邀请赛巅峰对决(HC6) nternation Individual Thinking Round个人思考赛 Total of 10 questions,each worth 10 points,for a total of 100 points. Time limit:30 minutes No discussion allowed.Each person answers one exam paper and submits one answer sheet. 共10道题，每题10分，共100分。 限时：30分钟。 不允许讨论，每人答一份试卷，各提交一份答题卡。 I-1.In the group stage of the World Cup,the four teams within each group play a round-robin tournament.Each team plays three matches.A win earns 3 points,a draw earns 1 point,and a loss earns 0 points.How many different possible point totals can a team obtain? 在世界杯小组赛中，每个小组内的4支球队进行单循环比赛，每支球队各踢 3场，胜一场积3分，平一场积1分，负一场积0分。一支球队可能获得的 积分分值共有多少种可能？ I-2.A new operation symbol s“@”is defined with the rule a@b=3×at2×b, Operations of the same level are calculated from left to right.Given that (x@4)@5-79,find the value of x. 定义新运算符号“@”，运算规则为a@b=3×a+2×b,同级运算按从左至右 顺序计算。已知(x@4)@5=79,那么x的值是多少？ Mathematics mvitational International Hope Cup I-3.An equilateral triangle is divided into two parts with equal perimeters.If the area of the shaded part is 168,what is the area of the unshaded part? 将一个等边三角形分割成周长相等的两部分，其中阴影部分的面积是168， 则空白部分的面积是多少？ I-4.A circular track has a circumference of 400 meters.Albert and Brandy start simultaneously from the same point on the track and run in opposite directions. Albert's speed is 6 meters per second,and Brandy's speed is 4 meters per second. Calvin starts at the same time from another point on the track,running at a speed of 5 meters per second.Twenty seconds after Calvin starts,he first meets Albert head-on.How many seconds after Calvin starts will he first meet Brandy? 环形跑道周长400米，A1bet和Brandy二人从跑道同一点同时反向出发， Albert的速度为每秒6米，Brandy的速度为每秒4米；Calvin从跑道另一处 同时出发，速度为每秒5米。Calvin出发20秒后第一次与A1bet迎面相遇， 那么Calvin出发后经过多少秒第一次与Brandy相遇？ I-5.Using the digits 0,1,2,3,4,5,form six-digit numbers with no repeated digits. Arrange all the six-digit numbers that satisfy the condition in increasing order. What is the 301st number in the sequence? 用数字0、1、2、3、4、5组成没有重复数字的六位数，将所有符合条件的 六位数从小到大依次排列，第301个数是多少？ ational Hop nternationat 2 Mathematics invitational International Hope Cup I-6.In a right trapezoid ABCD,the length of the top base AD is 10 cm,and the length of the bottom base BC is 18 cm.After extending the top base AD by 6 cm and shortening the bottom base BC by 2 cm,the figure becomes a parallelogram.The area of the new figure is 40 square centimeters larger than the area of the original trapezoid.What is the area of the original right trapezoid ABCD? 在直角梯形ABCD中，上底AD长10厘米，下底BC长18厘米。将上底AD 延长6厘米、下底BC缩短2厘米后，图形变为平行四边形，且新图形面积 比原梯形大40平方厘米。原直角梯形ABCD的面积是多少平方厘米？ I-7.There are 7 people numbered 1 to 7 and 7 seats also numbered 1 to 7.Each person sits in exactly one seat.How many seating arrangements are there in which exactly two people sit in seats with the same number as their own? 现有7个编号1至7的人，7个编号1至7的座位，每人仅坐一个座位，则 恰好只有两人的编号与所坐座位编号相同的坐法有多少种？ I-8.In the following vertical multiplication,identical letters represent the same digit, and different letters represent different digits.What is the value of A+B+C+ D? 在下列竖式中，相同的字母代表相同的数字，不同的字母代表不同的数字， 则A+B+C+D的和是多少？ □□B c□ rnational Hope Cup International Hope Cup B D Mathematics vitational International Hope Cup 1.Emd Sophia haveot obeads 5 3 of Sophia's beads together make 8 beads.How many more beadsdoesne girl have than the other? Enna和Sophia一共有120颗彩，珠Emma彩珠的与pia彩珠的3共 8 82颗。两人的彩珠数量相差多少颗？ I-10.What is the four-digit number whose every digit is even and which is divisible by 5,7,and 9 simultaneously? 每一位数字均为偶数，且能同时被5,7,9整除的四位数是多少？ International Hope Cup International Hope c nternational Hope Cup International Hope Cup International Hope Cup Mathematics Invitational Answer (答案) Question 1-1 I-2 1-3 I-4 I-5 I-6 I-7 1-8 I-9 I-10 题目 Answer 9 5 216 220 324015 280 924 6 P 8820 答案 International Hope Cup International Hope Cup Hope Cup International Hope Cup International Hope C nternational Hope Cup International Hope Cup 5