2026年希望杯国际数学邀请赛巅峰对决（IHC6）个人思考赛六年级下学期试题

Mthemtics nitational International Hope Cup 2026 Global Peak Challenge (IHC 6) 2026希望杯国际数学邀请赛巅峰对决(HC6) 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 I 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 "@is defined with the rule a@b=3xa+2xb. Operations of the same level are calculated from left to right.Given that (x@4)@5=79,find the value ofx. 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？ HOPS International Hope Cup Mathematics Invitational 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，Albert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Albert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 301s 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？ 2 Matnemauie invitstionl Internatlonal Hope Cup 1-6.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.Afer extending the top base 11)by 6 cmn and shortening the bottom basc BCby 2 cm,the figure becomes a parallelogramn.The area of the new figure Is 40 square centimeters larger than the arca of the original trapezoid.What is the arca of the original right trapezoid ACD? 作直角梯形ABCD中，上底AD长I0佩米，下底BC长18佩米。将.上底D 延长6细米、下底BC缩知2佩米后，图形变为平行四边形，且所图形积 比原梯形大40平方凰米。原直角梯形AB心D的面积是多少平方厘米？ I-7.There are 7 pcople numbered I to 7 and 7 seats also numbered I to 7,Each person sits in cxactly one seat.How many scating arrangements are there in which exactly two pcople sit in seats with the same number as their own? 现行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 恰好贝打阴人的编乃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，相同的字母代丧相同的数字，不同的学母代状不同的数字， 则A+B+C+D的和是多少？ □□ B C D c☐ B B□□C Matemticsinvtational International Hope Cup I-9.Emma and Sophia have a total of 120 colorful beads. 5 。of Emma's beads and 8 of Sophia's beads together make 8 beads.How many more beads does one girl have than the other? Enma和Sophia一共有120颗彩珠，Ema彩珠的}与Sopia彩珠的共 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？