GATE 2026 DA – Question 3
The four pieces of a puzzle are shown in the figure below.
![Four black puzzle pieces. The first is a tall piece with a rounded bump and notches on its right side, the second is a wide trapezoid with a round bite out of its lower edge, the third is an arrow-like piece with a small wedge cut out of its left side, and the fourth is a small piece with two peaks.] Which one of the figures labelled as P, Q, R, and S can be constructed by using each of the four pieces only once without overlaps? [Figure: Four black squares P, Q, R and S, each with a white shape cut out of it: in P a round head with a long beak and a diamond-shaped body, in Q the head and body without the beak, in R the head and beak with a flat-bottomed body, and in S a tilted head with a beak and a diamond body.](/question-images/GATE_DA_2026_Q3.png)
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Show answer and explanation
Correct answer: (A) P
Explanation
The pieces together make up the black part of one of the squares, so the black area of the square must equal the total area of the four pieces. Measuring the black area of each piece and of each square on the same scale, the four pieces add up to 39 956 units. Square P has 39 843 (a difference of about 0.3 %), while Q has 40 720, S has 41 933 and R has 43 497, which are 1.9 %, 5 % and 9 % too much. The piece with the small wedge cut out also needs a beak-shaped notch, which Q does not have. Only P can be built from the four pieces.