Elections Combinatorics Problem
Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P1 day 1
November 9, 2024
combinatoricsnational olympiad
Problem Statement
The country OMEC is divided in regions, each region is divided in districts, and, in each district, people vote. Each person choose between or . In a district, a candidate's letter wins if it's the letter with the most votes. In a region, a candidate's letter wins if it won in most districts. A candidate is the new president of OMEC if the candidate won in most regions. The candidate can rearrange the people of each district in each region (for example, A moves someone in District M to District N in region 1), but he can't change them to a different region.
Find the minimum number of votes that the candidate needs to become the new president.