Forest and trees
In a 3×3 forest there are nine cells. Each cell can occupy a hunter, a tree, or be empty. How many hunters can be in the forest if no hunters can see any other hunter because there is a tree in the way?
The answer is four:
HTH
TTT
HTH
What about 4×4, 5×5, … forests?
Problem creator: Ken Duisenberg.
February 3rd, 2010 at 2:20 am
I don’t believe it is possible with 4×4 to get more than 4 in the forest.
HTTT
TTHT
HTTT
TTHT
or
HTTH
TTTT
TTTT
HTTH
There are a lot of seemingly extra trees in there but if any of those trees are replaced with hunters, we’ll break the rules.
For 5×5, I believe the answer is 9.
HTHTH
TTTTT
HTHTH
TTTTT
HTHTH
February 3rd, 2010 at 4:28 am
Consider the 2n x 2n forest. Divide it into an n x n arrangement of squares, each square being a 2×2 square of locations. No square can have 2 or more hunters, as they would be able to see each other. Thus no square can have more than 1 hunter, and the forest cannot have more than n² hunters.