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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.

This entry was posted on Wednesday, February 3rd, 2010 at 12:02 am and is filed under Problem. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

2 Responses to “Forest and trees”

  1. Michael Maguire Says:
    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

  2. Richard Sabey Says:
    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.

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