Question 7
Alex has a garden divided into a $4\times4$ square grid. He wants to choose some cells in which to plant trees, following these three rules:
- At most one tree may be planted in each cell.
- Each row and each column may contain at most one tree.
- Each diagonal shown by a dashed line below may contain at most one cell with a tree.
What is the greatest number of trees Alex can plant, and in how many ways can he do so?
- At most one tree may be planted in each cell.
- Each row and each column may contain at most one tree.
- Each diagonal shown by a dashed line below may contain at most one cell with a tree.
What is the greatest number of trees Alex can plant, and in how many ways can he do so?