5. There are five big trees and three paths in a park. It has been decided to plant a sixth tree so that there are the same number of trees on either side of each path.
In which region of the park should the sixth tree be planted?
A
B
C
$\mathrm{D}$
E
SOlUTION
B

The path running from the top of the park to the bottom has two trees to the left of it and three trees to the right of it on the diagram. Hence the sixth tree should be planted to the left of this path. The path running from the top left of the park to the bottom right has two trees above it and three trees below it on the diagram. Hence the sixth tree should be planted above this path. When we combine these observations, we can see that the sixth tree should be planted in the region labelled B. Note: this would also mean that there were the same number of trees on either side of the third path.