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(336) 4

Part of 1992 Tournament Of Towns

Problems(1)

set of 27 triangles can be divided into two parts of the same total area

Source: TOT 336 1992 Spring A S4 - Tournament of Towns

6/9/2024
Three triangles A1A2A3A_1A_2A_3, B1B2B3B_1B_2B_3, C1C2C3C_1C_2C_3 are given such that their centres of gravity (intersection points of their medians) lie on a straight line, but no three of the 99 vertices of the triangles lie on a straight line. Consider the set of 2727 triangles AiBjCkA_iB_jC_k (where ii, jj, kk take the values 11, 22, 33 independently). Prove that this set of triangles can be divided into two parts of the same total area.
(A. Andjans, Riga)
combinatoricsgeometrycombinatorial geometryareas