MathDB

There exists a point A on a cube - Nice one

Source: IMO LongList 1970 - P41

May 22, 2011

geometry3D geometrycombinatorics unsolvedcombinatorics

Problem Statement

Let a cube of side

1

be given. Prove that there exists a point

A

on the surface

S

of the cube such that every point of

S

can be joined to

A

by a path on

S

of length not exceeding

2

. Also prove that there is a point of

S

that cannot be joined with

A

by a path on

S

of length less than

2