The figure shows two 4-tile patterns. Either one or both of the patterns can…
2026
The figure shows two 4-tile patterns.
Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?
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Show answer & explanation
1. Analyze the building blocks: Both given patterns are composed of exactly 4 small square tiles.
2. Establish the core rule: Any new figure constructed without overlapping these blocks must have a total tile count that is perfectly divisible by 4.
3. Count the total tiles in each option: Option A = 2x4 (8 tiles), Option B = 3x4 (12 tiles), Option C = 3x5 (15 tiles), Option D = 4x5 (20 tiles).
4. Since 15 is not a multiple of 4, Option C cannot be formed.
Final Answer: Option C
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