There are n>2022 cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities {\it unlucky}, if it is impossible to color the airlines between them in two colors without monochromatic triangle (i.e. three cities A, B, C with the airlines AB, AC and BC of the same color). The set containing all the cities is unlucky. Is there always an unlucky set containing exactly 2022 cities? combinatoricsgraph theory