Titre du sujet
A colored polygon
Lycée Arago (Perpignan)
Colegiul National B.P. Hasdeu (Buzau, Roumanie)
A convex N-gone is divided into triangles by its diagonals (assuming that 3 diagonals never intersect in the same point). The triangles are colored in red and in blue so that two triangles with a common side always have different colors. Find, in terms of N, the greatest possible value of the difference between the amount of red triangles and the amount of blue ones.