PUMaC 2008 · 组合（B 组） · 第 3 题
PUMaC 2008 — Combinatorics (Division B) — Problem 3
题目详情
- (3 points) Draw a regular hexagon. Then make a square from each edge of the hexagon. Then form equilateral triangles by drawing an edge between every pair of neighboring squares. If this figure is continued symmetrically off to infinity, what is the ratio between the number of triangles and the number of squares?
解析
- Draw a regular hexagon. Then make a square from each edge of the hexagon. Then form equilateral triangles by drawing an edge between every pair of neighboring squares. If this figure is continued symmetrically off to infinity, what is the ratio between the number of triangles and the number of squares? 2 ( ANS: . Each vertex is next to 2 squares, 1 triangle, and 1 hexagon. Since the number of 3 2 1 1 vertices on a square is 4, = of the polygons are squares. Similarly, of the polygons are 4 2 3 1 2 triangles and of the polygons are hexagons, yielding as the answer. CB: AP) 6 3