Combinatorics · Combinatorial geometry · Pigeonhole principle · Dissections · Area bounds · Convexity · Extremal triangle
Can nine points, no three of them collinear, be placed inside the cross-shaped figure below (its boundary included) in such a way that whenever three of them span a triangle lying inside the figure, that triangle has area greater than \(2\)?
The dimensions of the figure are
\[ A_1A_2 = B_1B_2 = C_1C_2 = D_1D_2 = 2 , \]
\[ A_2A_3 = A_3B_1 = B_2B_3 = B_3C_1 = C_2C_3 = C_3D_1 = D_2D_3 = D_3A_1 = 1 . \]
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Serbian National Competition (Drzavno takmicenje) 2010, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source