Question 15
A beaver has nine trees of three different heights, three trees of each height. The three kinds are shown here.
Trees of the same kind have the same height, and different kinds have different heights. The beaver plants them in a 3×3 garden with each kind appearing exactly once in every row and column. Each sign around the garden records how many trees can be seen along that row or column from that side. A taller tree hides shorter trees behind it. The following example illustrates the signs and a side view.
In the actual garden, only some signs have been filled in, as shown below. What is the sum of all the numbers around the garden when all signs are filled in?
Trees of the same kind have the same height, and different kinds have different heights. The beaver plants them in a 3×3 garden with each kind appearing exactly once in every row and column. Each sign around the garden records how many trees can be seen along that row or column from that side. A taller tree hides shorter trees behind it. The following example illustrates the signs and a side view.
In the actual garden, only some signs have been filled in, as shown below. What is the sum of all the numbers around the garden when all signs are filled in?