Which piece, when fitted into Figure (X), completes the square with no gap and no overlap? A piece may be turned round.

Answer & explanation
Correct answer: option 1
The correct answer is Option (1) →

The missing part of the 3 × 3 square in Figure (X) covers 4 small squares. The piece that fits must have exactly this shape and size. The piece in Option (1) fills the gap exactly.

Option (2) — Incorrect. This piece has one small square less than the gap, so a space would be left in the square.
Option (3) — Incorrect. This piece covers as many small squares as the gap, but one of them is in a different place, so it does not fit the gap even when turned round.
Option (4) — Incorrect. This piece has one small square more than the gap, so it cannot fit into it.