2026希望杯国际数学邀请赛巅峰对决个人思考赛IHC4-I-英简四年级数学试题

2026 Global Peak Challenge (IHC 4) 2026希望杯国际数学邀情赛巅峰对决(HC4) 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.Calculate:6×505-5×606. 计算：6×505-5×606。 I-2.The sum of two numbers,A and B,is 630.A is twenty times B.What is the value ofA? 甲、乙两数之和为630，甲数是乙数的20倍。甲数是多少？ I-3.A workshop produces 999 handmade ornaments.Two craftsmen can complete 144 ornaments in 8 days.The remaining omnaments must be finished within 5 days.How many additional craftsmen are needed? 手工工坊制作999个手作摆件，2名匠人8天做好144个摆件，剩余摆件需 在5天内完工，需要增加多少名匠人？ I-4.A transparent die has the distribution of numbers of dots on its six faces as shown in the figure.The sum of the numbers of dots on any pair of opposite faces is 7. Since the die is transparent,when viewing it from one face,the opposite face can also be seen at the same time.When observing the die from one of its faces,what numbers of dots are possible to see? (Write down all possible numbers.) 一个透明的骰子，六个面的点数分布如图所示，且相对两个面上的点数和为 7。由于骰子是透明的，因此从一个面观察能同时看到这一组相对面上的点。 那么，从其中一个面观察，看到的点数可能是多少？（要求写出所有可能的 点数) ● ●0● 88 I-5.Alex runs back and forth along a straight east-west track.On the first run,Alex runs 4 meters east,on the second run,8 meters west;on the third run,12 meters east,on the fourth run,16 meters west,and so on,alternating directions while increasing the distance of each run by 4 meters after every turn.After Alex completes the 2026th run,how many meters is Alex from the starting point? A1x在一条东西走向的直线跑道往返跑步，第一次向东跑4米，第二次向西 跑8米，第三次向东跑12米，第四次向西跑16米，…如此交替方向跑， 每次转向后跑动距离依次增加4米。当A1x跑完第2026次后，距离出发点 多少米？ 2 I-6.This year,the age difference between the mother and Ethan is equal to the age difference between the grandfather and the mother.The sum of their ages this year is 108 years.Six years ago,the grandfather's age was 5 times Ethan's age at that time.How old is Ethan this year? 今年妈妈与Ethan的年龄差等于爷爷与妈妈的年龄差。已知三人今年年龄之 和是108岁，6年前爷爷的年龄是Ethan当时年龄的5倍，那么Ethan今年 的年龄是多少岁？ I-7.Some blocks are arranged into a solid square array.After removing 100 blocks, the remaining blocks can be arranged into a two-layer hollow square array,with the number of blocks on each side of the outermost layer remaining the same as in the original solid square array.How many blocks were there in the original solid square array? 用一些积木摆成一个实心正方形阵列，拿走100块积木后，剩余积木刚好可 以摆成一个两层的空心正方形阵列（最外层每边的积木数量和原来一致)。 原来的实心正方形阵列中一共有多少块积木？ I-8.The four vertices of a rectangle are labeled 4,B,C,and D.There are 4 colors available for coloring the vertices.Two vertices connected by a line segment cannot be colored the same color.Not all four colors need to be used.How many different coloring schemes are possible? 长方形四个顶点标记为A、B、C、D,现有4种颜色可为顶点染色，要求有 线段相连的两个顶点颜色不能相同，四种颜色不必全部使用，一共有多少种 染色方案？ B I-9.In the 2026 FIFA World Cup hosted by the United States,Canada,and Mexico, 48 teams participate.The tournament begins with a group stage,where 4 teams in each group play a single round-robin tournament.Each team plays one match against each of the other three teams in its group.After the group stage,32 teams advance to the knockout stage.In the knockout stage,each match eliminates one team until the champion is determined.In addition,there is a third-place playoff match.How many matches are played in total in the 2026 FIFA World Cup? 2026年一共有48支球队参加美加墨世界杯足球赛，先进行小组赛，每个小 组4支球队进行单循环赛，每支球队与同小组另外三支球队各比赛一场：小 组赛结束后选出32支球队进入淘汰赛，淘汰赛每场比赛淘汰一支球队，直 至决出冠军；此外还有一场三四名决赛。美加墨世界杯一共进行了多少场比 赛？ I-10.Replace the letters in the circles with the numbers 1 to 6,using each number exactly once.The sums of the numbers along the three sides of the triangle must form an arithmetic sequence with a non-zero common difference.Given that A must be replaced by the number 6,how many possible number assignments satisfy the conditions? 用数字16分别替换圆圈中的字母，每个数字只用一次，要求三角形三边上 的数字和构成公差不为0的等差数列，其中A只能用数字6替换。符合条件 的数字替换字母的方案一共有多少种？ B Answer (答案) Question I-1 1-2 I-3 1-4 1-5 I-6 I-7 I-8 I-9 1-10 题目 Answer 0 600 17 5,7 4052 16 196 84 104 20 答案