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To create rectangles using 24 square pieces of wood, you need to find pairs of factors of 24 that represent the rectangle's dimensions. The possible dimensions are: 1x24, 2x12, 3x8, and 4x6. Each pair corresponds to a unique rectangle configuration, with the area of each rectangle equaling 24 square units. Thus, the different rectangle arrangements are 1x24, 2x12, 3x8, and 4x6.

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