Select the figure that will logically complete the series and replace the…
2023
Select the figure that will logically complete the series and replace the question mark (?).
Attempted by 2 students.
Show answer & explanation
In a figure-series question, three independent channels evolve together from one term to the next: (a) the outer/main shape and its shading, (b) the small appended shapes' position and colour, and (c) the shape and shading of the motif inside the outer shape. The next figure in the series must continue every one of these channels consistently, not just one of them.
Outer shape and shading: the outer shape cycles square (hatched) -> circle (plain) -> triangle (hatched), so the fourth term must return to a square, and since the shading has alternated hatched/plain/hatched, the fourth outer square must be plain (unhatched).
Appended shapes: each figure carries one matching pair of identically-styled appendages plus a single differently-styled 'odd' appendage. In the square figure the odd appendage sits at the top and is hatched while the pair (left and right) is black; in the circle figure the odd appendage moves to the bottom and turns black while the pair (left and right) becomes hatched. The odd appendage's colour is therefore alternating hatched -> black, so on the fourth (square) term the odd appendage must be black, positioned like the first square's odd appendage (at the top), while the pair returns to hatched at the left and right.
Inner motif: the shading of the inner motif alternates unhatched (circle) -> hatched (diamond) -> unhatched (square), so the fourth inner motif must be hatched; nothing in the first three terms forces one particular hatched outline over another, so this channel narrows the choice to any hatched motif rather than pinning down its exact shape.
Putting the first two channels together, the missing figure must be an unhatched outer square, with a lone black appendage at the top and a matching hatched pair at the left and right; the third channel additionally requires a hatched (not solid-filled, not outline-only) motif inside.
Term | Outer shape | Outer shading | Odd appendage | Pair appendage | Inner motif |
|---|---|---|---|---|---|
A | Square | Hatched | Top - hatched | Left/Right - black | Circle - unhatched |
B | Circle | Unhatched | Bottom - black | Left/Right - hatched | Diamond - hatched |
C | Triangle | Hatched | Bottom - hatched | Two corners - black | Square - unhatched |
? (answer) | Square | Unhatched | Top - black | Left/Right - hatched | Triangle - hatched |
The figure with a circular outer shape and small-circle-and-triangle appendages does not return to a square outline at all, so it fails the outer-shape cycle regardless of its interior.
The figure with an unhatched square outer shape but a solid black inner square and a mismatched solid/hollow circle pair breaks both the inner-shading alternation (should be hatched, not solid) and the matching-pair rule (the two side pieces must be identical).
The figure with a triangle outer shape repeats the third term's outline instead of advancing to a square, and its side appendages (a hollow circle and a solid triangle) do not form the required matching pair plus single odd piece.
Only the figure with a plain square outline, a lone black square on top, a hatched pair at the sides, and a hatched motif inside (here, a hatched triangle) satisfies every channel simultaneously, confirming it as the correct completion of the series.