Some of the parts shown below make a complete square when they are fitted together. Which set of parts does this? (Parts may be turned round.)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (D) 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), (D) and (E) fill a 4 × 4 square when (A) is turned through 180°, (D) is turned through 90° anticlockwise and (E) is turned through 90° anticlockwise.
Option (1) — Incorrect. (B) has as many small squares as (E) 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 (2) — Incorrect. (C) has as many small squares as (A) but one of them is in a different place. Together (A), (C) and (E) cover 15½ 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 (4) — Incorrect. (B) has as many small squares as (E) but one of them is in a different place. Together (A), (B) and (E) cover 17½ small squares, while the 4 × 4 square has 16, so they cannot make it; they cannot be fitted into any other complete square either.