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 2
The correct answer is Option (2) → (A), (B), (C) and (E) only
Parts form a complete square only if, placed side by side, they fill the square exactly, with no gap and no overlap. (A), (B), (C) and (E) fill a 5 × 5 square when (A) is turned through 90° clockwise, (C) is turned through 90° clockwise and (E) is turned through 180°.
Option (1) — Incorrect. (D) has as many small squares as (B) but one of them is in a different place. Together (A), (B), (C) and (D) cover 24½ small squares, while the 5 × 5 square has 25, so they cannot make it; they cannot be fitted into any other complete square either.
Option (3) — Incorrect. (D) has as many small squares as (B) but one of them is in a different place. Together (B), (C), (D) and (E) cover 23½ small squares, while the 5 × 5 square has 25, so they cannot make it; they cannot be fitted into any other complete square either.
Option (4) — Incorrect. (D) has as many small squares as (B) but one of them is in a different place. (A), (C), (D) and (E) cover as many small squares as the 5 × 5 square, but they cannot be fitted into it, or into any complete square, without a gap or an overlap.