assign 0 and 1 at 99 collinear points
Source: XI May Olympiad (Olimpiada de Mayo) 2005 L1 P3
September 22, 2022
combinatorics
Problem Statement
A segment of length is divided into little segments of length by intermediate points. Endpoint is assigned and endpoint is assigned . Gustavo assigns each of the intermediate points a or a , at his choice, and then color each segment of length blue or red, respecting the following rule:
The segments that have the same number at their ends are red, and the segments that have different numbers at their ends are blue. Determine if Gustavo can assign the 's and 's so as to get exactly blue segments. And blue segments? (In each case, if the answer is yes, show a distribution of 's and 's, and if the answer is no, explain why).