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
Count the distinct edge types on the four pieces (one curve pair, one jagged edge, one spike) and check which candidate figure shows exactly that many of each, no extra bumps or missing spikes.
This question checks visual assembly, fitting four irregular black pieces together, edge to edge with no gaps and no overlaps, to recreate one of the four candidate silhouettes. The four given pieces are a rounded piece with a smooth curved bite cut into one edge, a dome shaped piece with a matching curved notch, a piece with a jagged zig-zag edge, and a piece shaped like twin triangular peaks (a small peak beside a taller one).
Each candidate silhouette (P, Q, R, S) shows a bird-like outline: a round head, a pointed beak on the right, and an angular body below, joined by a jagged little step where the head meets the body. The four pieces must combine, without stretching past what their true edges allow, to trace out that exact outline.
Figure P: the beak here is one clean, straight-edged spike. This is exactly what you get when the taller peak of the twin-peaked piece becomes the beak, while its smaller peak tucks neatly inside the curved bite of the rounded piece, hidden from the outline. The jagged piece supplies the small step at the neck, and the dome piece rounds off the shoulder. Every edge of every piece lines up with a matching edge on another piece, so the four pieces close up perfectly with nothing left over and nothing overlapping.
Figure Q: there is no beak at all here, just a small stepped notch where a beak should be. Since one of the four pieces is a long pointed spike, that spike has to appear somewhere on the outer boundary of the assembled shape. Q's outline has nowhere for that spike to go, so it cannot be built from these four pieces.
Figure R: the beak is present, but there is extra jagged detail right where the beak meets the head, more notches than the pieces can actually produce at that joint. Forcing the pieces together this way leaves a mismatched edge, so R cannot be assembled without a gap or overlap.
Figure S: the notch near the beak is shaped like a star or crown with an extra upward spike, again more detail than the boundary of the four pieces can supply at that single joint. This extra spike does not correspond to any edge on the four pieces, so S is not achievable either.
Only Figure P uses every edge of the four pieces exactly once, in a way that closes up cleanly with no leftover gaps or overlaps.
Let's summarize:
Match curved edges to curved edges and straight edges to straight edges across the four pieces before checking any candidate figure.
A candidate that shows a spike or notch the pieces cannot produce (Q's missing beak, R and S's extra jagged detail) can be ruled out immediately.
Figure P is the only outline that the four pieces trace out exactly.
