The four pieces of a puzzle are shown in the figure below. 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?
Show Hint
Match each piece's jagged edges and peaks to the candidate outline that uses all four pieces exactly once, with no gaps or overlaps.
This is a picture assembly (mental jigsaw) question: four irregular pieces must combine, without turning any piece into a mirror image, without overlaps and without gaps, into exactly one of the four candidate outlines P, Q, R, S.
P: tracing the boundary of the four pieces around this outline, every jagged notch and every peak on the pieces lines up with a matching notch or peak on the neighbouring piece, so the four pieces close up perfectly with none left over and no gap remaining.
Q: this outline looks close to correct at first glance, but the beak portion is a touch too short for the scalloped piece to fill exactly, so fitting the pieces here leaves a sliver either overlapping two pieces or leaving a gap in the outline.
R: here the crest at the top does not match the twin-peak piece's exact width, so one of the pieces would have to stretch or rotate out of shape to close the gap, which is not allowed.
S: this outline shows one extra spike along the crest that none of the four given pieces can supply, since together the pieces only ever produce two peaks there, not three.
Since only outline P uses every edge of the four pieces exactly once with no leftover gap or overlap, P is the figure that the four pieces build.
Let's summarize:
Match each piece's distinctive notch or peak to a candidate's outline before picking an answer.
Reject any candidate where a piece would need to stretch, rotate wrongly, or leave a gap.
