MathDB

In an art museum,

n

paintings are exhibited, where

n \geq 33.

In total,

15

colors are used for these paintings such that any two paintings have at least one common color, and no two paintings have exactly the same colors. Determine all possible values of

n \geq 33

such that regardless of how we color the paintings with the given properties, we can choose four distinct paintings, which we can label as

T_1, T_2, T_3,

and

T_4,

such that any color that is used in both

T_1

and

T_2

can also be found in either

T_3

T_4

Problem Statement