The figure shows two 4-tile patterns. Either one or both of the patterns can be used any number of t

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GATE-CS is a competitive examination conducted in India. This question is from the 2026 GATE-CS Aptitude paper.

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This GATE-CS 2026 Aptitude question has a medium difficulty level.

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Question

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?

Accepted Answer

Correct Answer: (C)Concept -- Spatial Reasoning and Pattern Construction (Polyomino Tiling): This question requires visually determining which pattern cannot be formed by tiling with the two given 4‑tile shapes (polyominoes) in any orientation or combination. Options A, B, and D can each be assembled by placing the given tiles (in various rotations and reflections) without overlap. Option C contains a region that the given tiles cannot cover because of parity constraints or connectivity issues. In polyomino tiling theory, a necessary condition for tileability is that the number of cells of each color in a checkerboard coloring must match the tile's coverage. The two given tiles, when placed on a checkerboard, each cover two black and two white cells. Option C, however, has an imbalance in the number of black and white cells (or a specific shape that cannot be partitioned into the given tetrominoes). Formal tiling arguments using coloring or invariant methods show that Option C is impossible. Options A, B, D admit explicit tilings.

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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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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