MathDB

IMO LongList 1967, Socialists Republic Of Czechoslovakia 6

Source: IMO LongList 1967, Socialists Republic Of Czechoslovakia 6

December 16, 2004

geometrypoint setSequenceIMO ShortlistIMO Longlist

Problem Statement

Given a segment

AB

of the length 1, define the set

M

of points in the following way: it contains two points

A,B,

and also all points obtained from

A,B

by iterating the following rule: With every pair of points

X,Y

the set

M

contains also the point

Z

of the segment

XY

for which

YZ = 3XZ.