MathDB
Good Points and Segments

Source: Greek Mathematical Olympiad 2011 - P2

May 13, 2011
analytic geometrycombinatorics unsolvedcombinatorics

Problem Statement

In the Cartesian plane OxyOxy we consider the points A1(40,1),A2(40,2),…,A40(40,40){A_1}\left( {40,1} \right), {A_2}\left( {40,2} \right), \ldots , {A_{40}}\left( {40,40} \right) as well as the segments OA1,OA2,…,OA40O{A_1},O{A_2},\ldots,O{A_{40}}. A point of the Cartesian plane OxyOxy is called "good", if its coordinates are integers and it is internal of one segment OAi,i=1,2,3,…,40O{A_i}, i=1,2,3,\ldots,40. Additionally, one of the segments OA1,OA2,…,OA40O{A_1},O{A_2},\ldots,O{A_{40}} is called "good" if it contains a "good" point. Find the number of "good" segments and "good" points.
Back to ProblemsView on AoPS