3
Group the given figures into three categories, using each figure exactly once.
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Solution: Step 1: Identify figures that represent objects having both a base and an upper lid. Figures 5, 8, and 9 belong to this group.
Step 2: Identify figures that represent objects having a base but no upper lid. Figures 2, 3, and 6 fit this description.
Step 3: Identify figures that represent objects having neither a base nor an upper lid attached. Figures 1, 4, and 7 form the third category.
6
From the given figures, pinpoint the one that deviates from the common rule.
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Solution: Step 1: Identify and count the different types of elements (e.g., '=', circles, 'C'-shaped, 'V' signs) present in each figure.
Step 2: For figures (1), (2), (4), and (5), observe that the counts of different types of elements are arranged in an ascending sequence (e.g., 3, 4, 5, 6 in figure (1)).
Step 3: Apply this counting and sequence analysis to figure (3).
Step 4: Conclude that only in figure (3) do the numbers of different types of elements not form a consistent sequence.
Step 5: Therefore, figure (3) is the different one.
11
Group the provided figures into three categories, utilizing each figure only once.
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Solution: Step 1: Identify figures where the outer element is a rectangle with its two diagonals, and an additional element (similar or different) is placed inside. Figures 1, 5, and 7 form this class.
Step 2: Identify figures where the outer element is a triangle with its three medians, and an additional element (similar or different) is placed inside. Figures 2, 6, and 9 belong to this group.
Step 3: Identify figures where the outer element is a circle with its two mutually perpendicular diameters, and an additional element (similar or different) is placed inside. Figures 3, 4, and 8 comprise the third category.
12
Categorize the given figures into three groups, ensuring each figure is used precisely once.
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Solution: Step 1: Identify figures that contain similar elements (not equal in size), each divided into four parts and attached to each other. Figures 1, 4, and 8 meet this criterion.
Step 2: Identify figures that contain three elements, with two of them being similar, placed one inside the other. Figures 2, 5, and 6 fit this description.
Step 3: Identify figures that contain one element inside another, regardless of whether they are similar. Figures 3, 7, and 9 form the third category.
15
Classify the provided figures into three categories, ensuring each figure is used just once.
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Solution: Step 1: Identify figures that are composed of both straight and curved lines. Figures 1, 6, and 8 fit this characteristic.
Step 2: Identify figures that are closed and shaded by oblique line segments. Figures 3, 7, and 9 belong to this group.
Step 3: Identify figures that are composed solely of straight lines. Figures 2, 4, and 5 form the third category.
17
Classify the given figures into three distinct groups, ensuring each figure is used only once.
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Solution: Step 1: Identify figures that are two-dimensional quadrilaterals. Figures 1, 4, and 7 fall into this category.
Step 2: Identify figures that are three-dimensional. Figures 2, 5, and 8 belong to this group.
Step 3: Identify figures that are two-dimensional triangles. Figures 3, 6, and 9 form the third group.