MathDB

Call a set of

n

lines good if no

3

lines are concurrent. These

n

lines divide the Euclidean plane into regions (possible unbounded). A coloring is an assignment of two colors to each region, one from the set

\{A_1, A_2\}

and the other from

\{B_1, B_2, B_3\}

, such that no two adjacent regions (adjacent meaning sharing an edge) have the same

A_i

color or the same

B_i

color, and there is a region colored

A_i, B_j

for any combination of

A_i, B_j

.
A number

n

is colourable if there is a coloring for any set of

n

good lines. Find all colourable

n

Problem Statement