资源简介

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。
First Round第一轮
TS-1-1. In a convex quadrilateral, the lengths of two of its sides and its two diagonals
are all equal to 2026. What is the measure, in degrees, of the largest possible
interior angle of the quadrilateral
在一个凸四边形中，两条边的长与两条对角线的长均为 2026，该四边形的最
大内角为多少度？
TS-1-2. There are 16 stones in a pile. Allen and Bob take turns removing stones,
with Allen going first. On each turn, a player may remove only a prime number
of stones. If there are 0 or 1 stones remaining at the start of a player's turn, that
player has no legal move and loses. How many stones should Allen remove on
his first move to guarantee a win
共有 16颗石子，Allen和 Bob两人轮流取石子，每次只能取质数颗石子；剩
余石子为 0颗或 1颗时，轮到的人无法取石子则判定为输。若由 Allen先取
石子，Allen第一次应取多少颗石子能保证必胜？
1
TS-1-3. Fill the circles in the diagram with the numbers 1 through 8, using each
number only once. Let dn be the distance between the centers of the circles
containing the numbers n and n+1 (where n is 1 through 7), and d2 be the distance
between the centers of the circles containing the numbers 2 and 3. If the filling
order satisfies d1marked with a " "
将数字 1~8分别填入图中各个圆圈，每个数字仅使用一次。规定 dn为数字 n
和数字 n+1所在圆的圆心距离（n 为 1~7），如 d2为数字 2和 3所在圆的圆心
距离。若填法满足 d1哪个数字？
TS-1-4. Given that n is a positive integer, and n! + 76 is a perfect square. Find the
maximum value of n.
已知 n 是正整数，n! + 76是完全平方数，求 n 的最大值。
TS-1-5. As shown in the figure, right trapezoid ABCD is formed by joining two
isosceles right triangles ABC and ACD. Points E and F lie on line segments AB
and BC respectively, and CE⊥DF. Given CF=20 and AE=26, find the area of
right trapezoid ABCD.
如图，直角梯形 ABCD 由两个等腰直角三角形 ABC 和 ACD 拼接而成，点 E，
F 分别在线段 AB，BC 上，且 CE⊥DF。已知 CF=20，AE=26，求直角梯形
ABCD 的面积。
TS-1-6. In how many different ways can a 2×10 board be completely tiled with 1×2
dominoes, without overlaps or gaps
使用 1×2的多米诺骨牌无重叠、无空隙铺满 2×10的棋盘，共有多少种不同
的铺设方法？
2
Answer（答案）
Question TS-1-1 TS-1-2 TS-1-3 TS-1-4 TS-1-5 TS-1-6
题目
Answer 150 7 4 5 1944 89
答案
3

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