MathDB
Digging holes

Source: 2021 Korea Winter Program Test1 Day1 #4

February 3, 2021
combinatoricsgeometrycombinatorial geometry

Problem Statement

A positive integer m(≥2m(\ge 2) is given. From circle C1C_1 with a radius 1, construct C2,C3,C4,...C_2, C_3, C_4, ... through following acts: In the iith act, select a circle PiP_i inside CiC_i with a area 1m\frac{1}{m} of CiC_i. If such circle dosen't exist, the act ends. If not, let Ci+1C_{i+1} a difference of sets Ci−PiC_i -P_i. Prove that this act ends within a finite number of times.
Back to ProblemsView on AoPS