Which of the options can be made using the rubber stamp shown in the figure?
Show Hint
When solving stamp problems, deconstruct the target pattern into potential impressions of the original stamp. Pay close attention to how overlaps and intersections create new shapes. Also, check for features in the target that are impossible to create with the stamp (e.g., empty spaces where the stamp is solid).
Step 1: Understanding the Concept:
This problem requires us to determine which of the complex patterns can be generated by repeatedly using the given rubber stamp. This may involve rotating, translating, and overlapping the stamp's impression. We need to analyze the geometry of the stamp and see if it can be a "building block" for the patterns in the options.
Step 2: Detailed Explanation:
The stamp has a central solid part and four arms. It has two axes of symmetry (vertical and horizontal).
Option A: This pattern is made of four shapes arranged around a center. However, the stamp has a solid central piece. The pattern in A has an empty center. To create this, one would need a stamp without the central part, which is not what is given. Therefore, A cannot be made.
Option B: This star-like pattern can be created by overlapping two impressions of the stamp. One impression is in the standard orientation, and the second is rotated by 45 degrees and stamped on top of the first. The sharp points of the star are formed by the intersection of the concave inner edges of the stamp's arms. This is a possible construction.
Option C: This pattern can be created by overlapping two impressions of the stamp. The first is in the standard orientation, and the second is rotated by 90 degrees. The arms of the two impressions interlock to form the final shape. This is a possible construction.
Option D: This pattern contains thin, sharp elements and internal shapes that do not correspond to the geometry of the given stamp. The way the components connect does not seem achievable by simple stamping and overlapping. Therefore, D cannot be made with the given stamp.
Step 3: Final Answer:
The patterns in options B and C can be successfully created by rotating and overlapping the impression of the given rubber stamp.
