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1

Part of 1993 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1993 Problem 1.1

Source: Bundeswettbewerb Mathematik 1993 Round 1

10/9/2022
Every positive integer n>2n>2 can be written as a sum of distinct positive integers. Let A(n)A(n) be the maximal number of summands in such a representation. Find a formula for A(n).A(n).
combinatoricsSumsummandIntegers
coloring vertices of nonagon using 2 colors

Source: 1993 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1

11/20/2022
In a regular nonagon, each vertex is colored either red or green. Three corners of the nonagon determine a triangle. Such a triangle is called red or green if all its vertices are red or green if all are green. Prove that for each such coloring of the nonagon there are at least two different ones , that are congruent triangles of the same color.
combinatoricscombinatorial geometryColoring