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2026 Global Peak Challenge(IHC 8)
2026 希望杯国际数学邀请赛巅峰对决（IHC 8）
Team Speed Rounds 团队速度赛
There are a total of 12 questions, divided into two rounds with 6 questions each. Each
question is worth 10 points, for a total of 120 points.
Time limit: Round 1 - 10 minutes; Round 2 - 10 minutes.
Discussion is allowed. Each team will answer one set of question papers and submit
only one answer sheet.
共 12 道题，分两轮进行，每轮 6题，每题 10 分，共 120 分。
限时：第 1轮，10 分钟；第 2轮，10 分钟。
允许讨论，每个队答一份试卷，只提交一份答题卡。
Second Round 第二轮
TS-2-1. If two distinct numbers are chosen at random from the eight numbers below,
what is the probability that their product is greater than or equal to 0
从下面的 8个数中任选 2个不同的数，这 2个数的乘积不小于 0的概率是多
少？
－1、1、－2、2、－4、4、0、6
TS-2-2. As shown in the figure, the area of the shaded region in the left diagram is 12.
Given that a, b, x, and y satisfy ay=bx+20 and ax=by+26, find the area of the
shaded region in the right diagram.
如图，已知左图阴影部分的面积为 12，且 a，b，x，y满足 ay=bx+20，ax=by+26，
求右图阴影部分的面积。
1
TS-2-3. A positive integer n has exactly 2026 positive divisors. What is the
maximum possible number of positive divisors of n2？
设正整数 n恰好有 2026个正因数，则 n2最多有多少个正因数？
TS-2-4. There are four distinct prime numbers. The sum of any three of these prime
numbers is still a prime number. Find the minimum possible value of the sum of
the four prime numbers.
有四个互不相同的质数，其中任意三个质数相加的结果仍为质数，求这四个
质数和的最小值。
TS-2-5. As shown in the figure, rectangle ABCD is divided into 13 identical small
rectangles. Given that DE = 2 and DF = 2.5, find the value of DB .
如图，矩形 ABCD被分割为 13个完全相同的小矩形，已知 DE=2，DF=2.5，
求 DB2的值。
TS-2-6. Three distinct prime numbers less than 50 are selected. The product of these
three prime numbers must be divisible by their sum. How many different
selections are possible
选取三个小于 50且互不相同的质数，要求这三个质数的乘积能被它们的和
整除，有多少种不同的选法？
2
Answer（答案）
Question TS-2-1 TS-2-2 TS-2-3 TS-2-4 TS-2-5 TS-2-6
题目
Answer 4
答案 23 6075 48 130 14
7
3

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