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GATE 2026 CS (CS1) – Question 2

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 1 mark · Multiple choice

The figure shows two 4-tile patterns (a 2x2 square tile and an L-tromino with an extra corner tile). 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?

  1. Pattern with 12 tiles formed by three 4-tile blocks
  2. Pattern with 16 tiles formed by four 4-tile blocks
  3. Pattern with 20 tiles formed by five 4-tile blocks
  4. Pattern with an odd parity or incompatible boundary configuration

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Correct answer: (D) Pattern with an odd parity or incompatible boundary configuration

Explanation

Both given polyomino patterns consist of 4 squares (tetrominoes). Any region that can be tiled without overlap by these tetrominoes must have an area that is a multiple of 4. Furthermore, by standard checkerboard or parity coloring of the grid, pattern (D) produces an unbalanced color distribution that cannot be covered by the given shapes. Hence, option (D) cannot be constructed.