Spring flower garden
Source: Vietnam TST 2024 P2
March 27, 2024
combinatorics
Problem Statement
In a garden, which is organized as a board, we plant three types of flowers: roses, daisies, and orchids. We want to plant flowers such that the following conditions are satisfied:(i) Each grid is planted with at most one type of flower. Some grids can be left blank and not planted.
(ii) For each planted grid , there exist exactly other planted grids in the same column or row such that those grids are planted with flowers of different types from 's.
(iii) Each flower is planted in at least grid. What is the maximal number of the grids that can be planted with flowers?