Comments on: Forest and trees http://easyquestion.net/thinkagain/2010/02/03/forest-and-trees/ mathematical dialogues aimed to confuse Wed, 07 Mar 2012 22:43:23 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Richard Sabey http://easyquestion.net/thinkagain/2010/02/03/forest-and-trees/#comment-43278 Richard Sabey Tue, 02 Feb 2010 21:28:33 +0000 http://easyquestion.net/thinkagain/?p=2685#comment-43278 Consider the 2n x 2n forest. Divide it into an n x n arrangement of squares, each square being a 2x2 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. 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.

]]> By: Michael Maguire http://easyquestion.net/thinkagain/2010/02/03/forest-and-trees/#comment-43274 Michael Maguire Tue, 02 Feb 2010 19:20:21 +0000 http://easyquestion.net/thinkagain/?p=2685#comment-43274 I don't believe it is possible with 4x4 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 5x5, I believe the answer is 9. HTHTH TTTTT HTHTH TTTTT HTHTH 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

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