HMMT 二月 2002 · GEN1 赛 · 第 8 题
HMMT February 2002 — GEN1 Round — Problem 8
题目详情
- Count the number of triangles with positive area whose vertices are points whose ( x, y )- coordinates lie in the set { (0 , 0) , (0 , 1) , (0 , 2) , (1 , 0) , (1 , 1) , (1 , 2) , (2 , 0) , (2 , 1) , (2 , 2) } .
解析
- Count the number of triangles with positive area whose vertices are points whose ( x, y )-coordinates lie in the set { (0 , 0) , (0 , 1) , (0 , 2) , (1 , 0) , (1 , 1) , (1 , 2) , (2 , 0) , (2 , 1) , (2 , 2) } . ( ) 9 Solution: There are = 84 triples of points. 8 of them form degenerate triangles (the 3 ones that lie on a line), so there are 84 − 8 = 76 nondegenerate triangles.