MathDB

Consider

2n+1

points in space, no four of which are coplanar where

n>1

. Each line segment connecting any two of these points is either colored red, white or blue. A subset

M

of these points is called a connected monochromatic subset, if for each

a,b \in M

, there are points

a=x_0,x_1, \dots, x_l = b

that belong to

M

such that the line segments

x_0x_1, x_1x_2, \dots, x_{l-1}x_1

are all have the same color. No matter how the points are colored, if there always exists a connected monochromatic

k-

subset, find the largest value of

k

. (

l > 1

)

Problem Statement