AMC 8 1988 Problem 24
AMC8 1988 年第 24 题
变换与对称★★★★☆
The square in the first diagram "rolls" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram 4 ?
第一个图中的正方形围绕固定的正六边形顺时针"滚动"，直到到达底部。图 4 中实心三角形将位于哪个位置？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
A
解析 · Solution
解法1
常规解法 · 跟踪底边
盯住带三角形底边的那条边。方块每滚一步，这条边就换到方块的下一条边上；数到图 4 时，它落在方块的左侧，故选 A。
巧解 · 算转角
沿正六边形外缘滚，每步方块顺时针转 （ 直角加 外角）。到图 4 共转 ，原本朝上的三角形转到朝右，对应 A。
Solution 1
Elementary · track the base edge
Track the side carrying the triangle's base. Each roll moves it to the next side of the square; by diagram 4 it ends up on the left side of the square, so the answer is (A).
Slick · count the turning angle
Rolling around the hexagon, each step turns the square clockwise (a corner plus a exterior turn). By diagram 4 it has turned , so the upward triangle now points right, matching (A).
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