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Perceptual Puzzle #37- Fewest Fences -

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A square fence surrounds nine apple trees. What is the smallest number of additional square fences that must be added to completely separate the trees from each other (i.e. such that you can not go from one tree to another without crossing a fence)?
Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?