Problem

Source: 2021 Korea Winter Program Test1 Day1 #4

Tags: combinatorics, geometry, combinatorial geometry



A positive integer m(2) is given. From circle C1 with a radius 1, construct C2,C3,C4,... through following acts: In the ith act, select a circle Pi inside Ci with a area 1m of Ci. If such circle dosen't exist, the act ends. If not, let Ci+1 a difference of sets CiPi. Prove that this act ends within a finite number of times.