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GATE CSE 2026 Session 1 Q2: Which grid cannot be tiled by a 2×2 square and a 1×4 bar

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?

Top: a 2 by 2 square of tiles and a vertical bar of 4 tiles. Below: options (A) a 2 by 4 grid, (B) a 3 by 4 grid, (C) a 3 by 5 grid, (D) a 4 by 5 grid
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Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
Show answer and explanation

Answer: C (official GATE 2026 final answer key)

Concept used: A shape built from 4-tile pieces must have a number of tiles divisible by 4.

First step: Count the tiles in each grid: 8, 12, 15 and 20; only 15 is not a multiple of 4.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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