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2026 AMC8 #22 · Counting, Probability & Statistics · ★★★★★
The integers from 1 to 25 are arbitrarily separated into five groups of 5 numbers each. The median of each group is identified. Let M equal the median of the five medians. What is the least possible value of M?
将 1 到 25 的整数任意分成五组，每组 5 个数。找出每组的中位数，再求这五个中位数的中位数 M。M 的最小可能值是多少？

正确答案：A · 分值：1

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2025 AMC8 #25 · Counting, Probability & Statistics · ★★★★★
Makayla finds all the possible ways to draw a path in a 5×55 \times 5 diamond-shaped grid. Each path starts at the bottom of the grid and ends at the top, always moving one unit northeast or northwest. She computes the area of the region between each path and the right side of the grid. Two examples are shown in the figures below. What is the sum of the areas determined by all possible paths?
Makayla在一个5×5的菱形网格中找到了所有可能的绘制路径的方式。每条路径从网格底部开始，到网格的顶部结束，总是朝东北或西北方向移动一个单位。她计算了每条路径与网格右侧边缘之间的区域面积。下图展示了两个示例。请问所有可能路径与网格右侧边缘之间的区域面积之和是多少？

正确答案：B · 分值：1

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2024 AMC8 #23 · Geometry · ★★★★★
Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point (0, 4) to point (2, 0) and colors the 4 cells whose interiors intersect the segment, as shown below. Next Rodrigo draws a line segment connecting point (2000, 3000) to point (5000, 8000). Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?
Rodrigo有一张非常大的方格纸。他先画了一条线段连接点（O,4)和点（2,0），然后为内部与该线段相交的4个方格上色，如图所示。紧接着Rodrigo又画了一条线段连接点(2000,3000）和点（5000,8000)，并为内部与该线段相交的方格上色。 请问这次Rodrigo要给多少个方格上色？

正确答案：C · 分值：1

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2022 AMC8 #25 · Counting, Probability & Statistics · ★★★★★
A cricket randomly hops between 4 leaves, on each turn hopping to one of the other 3 leaves with equal probability. After 4 hops what is the probability that the cricket has returned to the leaf where it started?
一只蟋蟀随机地在 4 片叶子之间跳来跳去，每次都以相同的概率跳到其它的 3 片叶子上。问经过 4 次跳跃，蟋蟀回到它开始的那片叶子的概率是多少？

正确答案：E · 分值：1

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2019 AMC8 #24 · Geometry · ★★★★★
In triangle ABC , point D divides side AC‾\overline{AC} so that AD:DC=1:2 . Let E be the midpoint of BD‾\overline{BD} and let F be the point of intersection of line BC and line AE . Given that the area of △ABC\triangle ABC is 360 , what is the area of △EBF\triangle EBF?
在三角形 ABC 中，点 D 把边分成的两段满足 AD:DC＝1:2，点 E 是线段 BD 的中点，F 是直线 BC 和 AE 的交点。已知 ΔABC 的面积是 360，问 ΔEBF 的面积是多少？

正确答案：B · 分值：1

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2017 AMC8 #19 · Number Theory · ★★★★★
For any positive integer MM , the notation M! denotes the product of the integers 1 through MM . What is the largest integer nn for which 5n5^n is a factor of the sum 98!+99!+100! ?
对于任何正整数 M 来说，符号 M！表示从 1 到 M 的所有整数的乘积。使得 ＋100！的一个因子的最大整数 n 是多少？
是 98！＋99！

正确答案：D · 分值：1

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2007 AMC8 #22 · Geometry · ★★★★★
A lemming sits at a corner of a square with side length 10 meters. The lemming runs 6.2 meters along a diagonal toward the opposite corner. It stops, makes a 90∘90^{\circ} right turn and runs 2 more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?
一只旅鼠坐在一个边长为 10 米的正方形的某个角落里。旅鼠沿着对角线朝对面的角落跑了 6.2 米，然后停下来，右转 90 度，又继续跑了 2 米。一位科学家测量了旅鼠和正方形各边之间的最短距离。这四段距离的平均值是多少米？

正确答案：C · 分值：1

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