2026年希望杯国际数学邀请赛巅峰对决IHC8-TT团队思考赛八年级数学试题

International Hope Cup Mathematics Invitational 2026 Global Peak Challenge(IHC 8) 2026希望杯国际数学邀请赛巅峰对决(HC8) 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. 许讨论，每个队答一份试卷，只提交一份签您卡0。 共10道题，每题10分，共100分。 限时：45分钟。 TT-1.In the arithmetic expression TWO+ZERO+TWO+SIX=2026,the same letters represent the same digits,and different letters represent different digits.If I=9, find the value of the five-digit number WORST 在算式Twō+ZERO+Twō+S=2026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。若I=9,求五位数WORST的值。 TT-2.Given that Ais a nonzero natural number,and 26 times the sum of the digits of A is exactly equal to aitself find the sum of all possible values of A that satisfy the condition 已知A为非零自然数，若A各位数字之和的26倍恰好等于A本身，求所有 符合条件的A之和。 TT-3.If a natural number multiplied by 2025 has exactly 2025 positive divisors, what is the minimum possible number of positive divisors of the natural number? 如果一个自然数的2025倍恰有2025个正因数，这个自然数最少有多少个正 因数？ International Hope Cup Mathematics Invitational TT-4.Brother Rabbit,Little Brother Rabbit,and a turtle are having a race.The starting point A of the two rabbits is a certain distance behind the turtle's starting point B.All three start at the same time.Brother Rabbit runs the fastest and is the first to catch up with the turtle.At that moment,Little Brother Rabbit is still 40 meters behind them.The three continue running forward.When Little Brother Rabbit catches up with the turtle,Brother Rabbit is already 50 meters ahead of both of them.Little Brother Rabbit is not satisfied and shouts,"Let's start over!" In the rematch,the starting positions are adjusted:Little Brother Rabbit starts from the turtle's original starting point B,while Brother Rabbit and the turtle keep their original starting positions.Their speeds remain unchanged,and all three start at the same time.When Brother Rabbit catches up with Little Brother Rabbit,how many meters behind them is the turtle? 兔大哥、兔小弟和乌龟赛跑，两只兔子的起点A在乌龟起点B后方一段距 离，三者同时出发。兔大哥跑得最快，率先追上乌龟，此时兔小弟还落后他 们40米。三者继续向前奔跑，当兔小弟追上乌龟时，兔大哥已经领先二者 50米。免小弟不服，喊道：“重来！”于是重新比赛，本次调整出发位置：兔 小弟从乌龟原来的起点B出发，兔大哥与乌龟出发点保持不变，三者速度不 变，仍同时出发。那么当兔大哥追上兔小弟时，乌龟落后他们多少米？ TT-5.Use the three colors red,yellow,and blue to color the six regions in the figure below.The requirement is that for any four mutually connected regions (such as regions A,B,C,and D),all three colors-red,yellow,and blue-must appear among them.How many different coloring schemes are possible? 用红、黄、蓝三种颜色对下图六个区域染色，要求对于任意四个彼此相连的 区域（如区域A,B,C,D)内，必须同时包含红、黄、蓝三种颜色，一共 有多少种不同的染色方案？ Mtematics nitational International Hope Cup TT-6.Let a,b,and c be digits from 0 to 9,where b and c are not both 0 and not both 9.If the mixed repeating decimal represented by 0.abc(0.abcbcbcbc...)is reduced to its simplest fraction and the denominator is 55,how many ordered triples (a,b,c)satisfy the condition? 设4，b,c分别是0-9中的数字，且b,c不同时为0，也不同时为9。若混 循环小数0.abc化为最简分数后分母是55，则满足条件的有序数组(a,b, c)共有多少组？ TT-7.Charles has three types of candies with different flavors.He first counted the number of candies of each type.Then he ate 20 candies from each of the two types with the largest quantities.After that,he counted the remaining candies again and ate 16 candies from each of the two types that had the largest quantities at that time.Finally,he counted the remaining number of candies of each type. Charles noticed that in each of the three counts,the sum of the quantities of the two types of candies ranked in the top two was exactly three times the quantity of the third type of candy.What was the original total number of candies? Charles有三种口味的糖果，他先统计了糖果的数量，随后吃掉数量最多的 两种糖果各20颗：然后他又统计剩余糖果的数量，再吃掉此时数量最多的 两种糖果各16颗；接着再统计每种糖果的剩余数量。Charles发现，三次统 计每一次数量排名前二的两种糖果的数量之和，都等于第三种糖果数量的3 倍，那么最初三种糖果的总数量为多少颗？ TT-8.A natural number Nhas exactly 12 positive divisors.If the remainders obtained when these 12 positive divisors are divided by 20 are all distinct,find the minimum possible value of N. 自然数N恰有12个正因数，若这12个正因数除以20的余数互不相等，求 N的最小值。 International Hope Cup Mathematics Invitational TT-9.As shown in the figure,point O is the center of both equilateral triangles ABC and DEF.The line FO is drawn and extended to intersect AC at G and DE at H.If the area of equilateral triangle ABC is 210,and FH:HG-7:1,find the area of triangle EOG. 如图，己知O点是正三角形ABC和正三角形DEF的中心，连接FO并延长 交AC于G,交DE于H。如果三角形ABC的面积为210，且FH:HG=7:1, 求三角形EOG的面积。 al Hope Cup TT-10.The sequence 1,1,2,3,5,8,...,in which each term from the third term onward is the sum of the previous two terms,is called the Fibonacci sequence. The first 27 terms of the Fibonacci sequence are placed into the 27 cells of a 3x3x3 cube,with one number in each cell.Along each of the three dimensions-length,width,and height-the cube has 9 straight lines that pass through 3 cells,making a total of 27 such lines.The three numbers on each line are added together to obtain 27 sums.What is the maximum possible number of odd sums among these 27 sums? 数列1,1,2,3,5,8，…从第三项起，每一项都等于前两项之和，该数列 称为斐波那契数列。将斐波那契数列的前27项分别填入3×3×3立方体的27 个格子，每个格子填入一个数。立方体沿长、宽、高三个维度各有9条穿过 3个格子的直线，合计27条直线。将每条直线上3个数相加得到27个和， 这27个和里面最多能有多少个奇数？ Internationa International Hope Cup Mathematics Invitational Answer(答案) Question TT-1 题目 TT-2 TT-3 TT-4 TT-5 Answer 答案 36542 702 135 800 24 Question TT-6 TT-8 TT-9 题目 TT-7 TT-10 Answer 答案 40 112 108 26 24 International Hope Cup International Hope Cup al Hobe Cup International Hope Cup International Hope Cu nternational Hope Cup International Hope Cup