MathDB

M2741

Part of Kvant 2023

Problems(1)

distances between monochromatic points on a line

Source: ARO Regional stage 2023 10.9

2/16/2023
Given is a positive integer kk. There are nn points chosen on a line, such the distance between any two adjacent points is the same. The points are colored in kk colors. For each pair of monochromatic points such that there are no points of the same color between them, we record the distance between these two points. If all distances are distinct, find the largest possible nn.
combinatoricsRussia