Which of the following sets of parts can be fitted together, without gaps or overlaps, to make a complete square? The parts may be turned round.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B), (C) and (D) only
Parts form a complete square only if, placed side by side, they fill the square exactly, with no gap and no overlap. (B), (C) and (D) fill a 4 × 4 square when (B) is turned through 90° clockwise, (C) is turned through 90° clockwise and (D) is turned through 90° anticlockwise.
Option (1) — Incorrect. (A) has as many small squares as (C) but one of them is in a different place. Together (A), (C) and (D) cover 12½ small squares, while the 4 × 4 square has 16, so they cannot make it; they cannot be fitted into any other complete square either.
Option (2) — Incorrect. (A) has as many small squares as (C) but one of them is in a different place. (A), (B) and (D) cover as many small squares as the 4 × 4 square, but they cannot be fitted into it, or into any complete square, without a gap or an overlap.
Option (4) — Incorrect. (A) has as many small squares as (C) but one of them is in a different place. Together (A), (B) and (C) cover 14 small squares, while the 4 × 4 square has 16, so they cannot make it; they cannot be fitted into any other complete square either.