MathDB
[sum A_kB_k/2A_kB_k] where 2008 // lines divide ABC in 2008 equal areas

Source: Indonesia INAMO Shortlist 2009 G9 https://artofproblemsolving.com/community/c1101409_

December 11, 2021
floor functionequal areasgeometry

Problem Statement

Given triangle ABCABC. Let A1B1A_1B_1, A2B2A_2B_2,... ..., A2008B2008A_{2008}B_{2008} be 20082008 lines parallel to ABAB which divide triangle ABCABC into 20092009 equal areas. Calculate the value of ⌊A1B12A2B2+A1B12A3B3+...+A1B12A2008B2008⌋ \left\lfloor \frac{A_1B_1}{2A_2B_2} + \frac{A_1B_1}{2A_3B_3} + ... + \frac{A_1B_1}{2A_{2008}B_{2008}} \right\rfloor
Back to ProblemsView on AoPS