PUMaC 2009 · 组合（A 组） · 第 4 题
PUMaC 2009 — Combinatorics (Division A) — Problem 4
题目详情
- We divide up the plane into disjoint regions using a circle, a rectangle and a triangle. What is the greatest number of regions that we can get?
解析
- We divide up the plane into disjoint regions using a circle, a rectangle and a triangle. What is the greatest number of regions that we can get? Solution. 22. Looking at the triangle and rectangle first, we have at most 8 regions. Then the circle has at most 14 intersections with straight lines from triangle and rectangle, which means we add at most 14 regions by adding a circle, for a grand total of 22.