Select the option that can replace the question mark (?) and complete the…
2023
Select the option that can replace the question mark (?) and complete the given figure series.
Attempted by 6 students.
Show answer & explanation
Concept
In a pictorial series each panel is produced from the one before it by a seat rule: every symbol is carried from the seat it occupies to a fixed destination seat, and that same rule is reused at each step. When a single rule does not fit every step, the next thing to test is whether two rules alternate. To read a rule off two consecutive panels, simply note which seat the symbol sitting in each seat has moved to.
Application
Label the five seats that every panel uses: middle-left (ML), centre (C), top-right (TR), middle-right (MR) and bottom-right (BR). The same five symbols — ☆, ↑, K, L and D — occupy them once each in every panel.
Panel | ML | C | TR | MR | BR |
|---|---|---|---|---|---|
1 | ☆ | L | D | K | ↑ |
2 | K | D | ↑ | ☆ | L |
3 | ↑ | ☆ | L | D | K |
4 | D | L | K | ↑ | ☆ |
Panel 1 → Panel 2: ☆ goes ML→MR, L goes C→BR, D goes TR→C, K goes MR→ML and ↑ goes BR→TR. Call this seat rule P: ML→MR, C→BR, TR→C, MR→ML, BR→TR.
Panel 2 → Panel 3: K goes ML→BR, D goes C→MR, ↑ goes TR→ML, ☆ goes MR→C and L goes BR→TR. Call this seat rule Q: ML→BR, C→MR, TR→ML, MR→C, BR→TR.
Panel 3 → Panel 4: ↑ goes ML→MR, ☆ goes C→BR, L goes TR→C, D goes MR→ML and K goes BR→TR — that is rule P once more.
The two rules therefore alternate P, Q, P, …, so the step from Panel 4 into the question mark has to be rule Q.
Apply Q to Panel 4 (ML=D, C=L, TR=K, MR=↑, BR=☆): D goes ML→BR, L goes C→MR, K goes TR→ML, ↑ goes MR→C and ☆ goes BR→TR.
The missing panel is therefore ML=K, C=↑, TR=☆, MR=L, BR=D.
Cross-check
Performing P and then Q in succession composes into a single five-seat cycle ML→C→TR→MR→BR→ML, so across every two steps each symbol advances exactly one seat around that cycle. Test it on Panel 1 → Panel 3: ☆ ML→C, L C→TR, D TR→MR, K MR→BR and ↑ BR→ML, which reproduces Panel 3 term for term. Applying the same one-seat advance to Panel 3 (ML=↑, C=☆, TR=L, MR=D, BR=K) gives ML=K, C=↑, TR=☆, MR=L, BR=D — the same panel reached by an independent route.
The panel that completes the series therefore carries K at the middle-left, ↑ at the centre, ☆ at the top-right, L at the middle-right and D at the bottom-right.