Question 156
In a garden, which is organized as a $2024 \times 2024$ 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 cell is planted with at most one type of flower. Some cells can be left blank and not planted.
(ii) For each planted cell $A$, there exist exactly $3$ other planted cells in the same column or row such that those $3$ cells are planted with flowers of different types from $A$'s.
(iii) Each flower is planted in at least $1$ cell.
What is the maximal number of the cells that can be planted with flowers?
(i) Each cell is planted with at most one type of flower. Some cells can be left blank and not planted.
(ii) For each planted cell $A$, there exist exactly $3$ other planted cells in the same column or row such that those $3$ cells are planted with flowers of different types from $A$'s.
(iii) Each flower is planted in at least $1$ cell.
What is the maximal number of the cells that can be planted with flowers?