His majesty, the King of Cherryland, is the owner of a wonderful
park. This park is located between the palace and the pool (see
image below). A path (brown areas) leads from the palace to the
pool. There are no trees in the park yet, but the king plans to
set as much trees as possible in the park. He already bought 7
cherry-trees and he wants to have some apple-trees, too.
Unfortunately in Cherryland a strange law (in Cherryland
everything is a little bit crazy, see problem #32) exists:
'It is forbidden to have cherry-trees and apple-trees together
in the same row, column or diagonal in one's park.'
This law is demonstrated in the image below, where 'x' are the
forbidden positions for the apple-trees if the illustrated tree
was a cherry-tree. Of course cherry-trees are allowed on these
positions.
Now the king employs you to arrange the trees. What is maximum
number of apple-trees you can place in the park together with
7 cherry-trees without breaking the law?
Note: The path may not be changed and must be free of trees.
Correct answer: 7 trees
Explanation:
There are many arrangements possible. One is shown in the image below.
