Select the figure that will come in place of the question mark (?) in the…
2023
Select the figure that will come in place of the question mark (?) in the following figure series.
Attempted by 6 students.
Show answer & explanation
Concept: A figure series is built from a small number of attributes that vary independently of one another — the shape itself, how that shape is shaded, and any labels attached to the frame. Each attribute obeys its own rule as the row advances, so the dependable method is to isolate one attribute at a time, extend that single rule forward by one step, and only then recombine them. The frame that belongs in the empty slot is the one figure that satisfies every extended rule at the same time.
Application: Reading the four given frames attribute by attribute gives the following picture.
Frame | Points on the star | Shading | Letters and corners |
|---|---|---|---|
1 | 4 | Solid | A at top-left, B at bottom-right |
2 | 5 | Outline | B at top-right, C at bottom-left |
3 | 6 | Solid | D at top-left, C at bottom-right |
4 | 7 | Outline | E at top-right, D at bottom-left |
5 (missing) | 8 | Solid | E at top-left, F at bottom-right |
Number of points: 4, then 5, then 6, then 7 — one extra point at every step, so the missing frame holds an eight-pointed star.
Shading: solid, outline, solid, outline — the two treatments alternate, so the missing frame is shaded solid.
Letters: the pair advances by one letter of the alphabet each frame — A and B, then B and C, then C and D, then D and E — so the missing frame carries E and F.
Corner placement: the two labelled corners swing a quarter-turn anticlockwise at every step, which makes the occupied diagonal alternate between top-left/bottom-right and top-right/bottom-left. The letter carried over from the previous frame travels with that turn, and the corner emptied by the dropped letter receives the newly added letter. E stands at the top-right in the fourth frame, so the turn carries it to the top-left, and the new letter F takes the bottom-right.
Cross-check: Track only the carried-over letter across the row and the quarter-turn rule can be tested on its own: B moves from bottom-right to top-right, C from bottom-left to bottom-right, and D from top-left to bottom-left — each of those is exactly one quarter-turn anticlockwise. Applying the same turn to E sends it from top-right to top-left, which also restores the top-left/bottom-right diagonal used by frames 1 and 3, as the alternation demands. Combining all four rules, the frame that belongs in place of the question mark is an eight-pointed star shaded solid, carrying E at the top-left corner and F at the bottom-right corner. An eight-pointed star drawn in outline would break the solid/outline alternation, and a solid eight-pointed star whose letters sit on the top-right/bottom-left diagonal would break the quarter-turn rotation.