Problem 4. Is it possible to color all the diagonals of a regular 2015-gon using 2012 colors such that all the diagonals emanating from one vertex are of different colors?
Problem 4. Is it possible to color all the diagonals of a regular 2015-gon using 2012 colors such that all the diagonals emanating from a single vertex are of different colors?

| Solution | Criteria |
| :--- | :--- |
| Consider the diagonals of color 1. Note that |  |
| each diagonal connects two vertices. Since the | 5 points for the correct answer. |
| number of vertices is 2015, an odd number, and |  |
| one diagonal of color 1 emanates from each |  |
| vertex, there will be a vertex from which no |  |
| diagonal of color 1 emanates. |  |
| Answer. No. |  |