Select the figure from the options that can replace the question mark (?) and…
2023
Select the figure from the options that can replace the question mark (?) and complete the given pattern.
Attempted by 1 students.
Show answer & explanation
Concept — a letter series rearranges positions, not letters. Every term of such a series is built from the term before it by a fixed positional rule: a permutation that states which slot each letter moves into. The set of letters never changes; only the slots they occupy do. So any series of this kind is read by numbering the slots and describing each step purely as “the letter in slot i moves to slot j”. If one single permutation does not carry every step, the next thing to test is whether two permutations alternate — one acting on the 1st, 3rd, 5th … steps and the other on the 2nd, 4th, 6th … steps.
Application. Number the six slots 1 to 6 and read off what each step of the given series does.
Step 1, SLATED → ALSDET: the letters in slots 1 and 3 exchange places (S and A), and the letters in slots 4 and 6 exchange places (T and D); slots 2 and 5 (L and E) are left alone. Call this Rule A — exchange 1↔3 and exchange 4↔6.
Step 2, ALSDET → TELSDA: Rule A here would give back SLATED, so a second rule is at work. The two end letters exchange places (A goes to slot 6, T comes to slot 1), and the middle block L, S, D, E shifts one slot to the right as a cycle, the letter in slot 5 wrapping round into slot 2, so it reads E, L, S, D. Call this Rule B — exchange 1↔6 and rotate slots 2 to 5 one place right.
Step 3, TELSDA → LETADS: slots 1 and 3 exchange (T and L), slots 4 and 6 exchange (S and A), and slots 2 and 5 (E and D) stay put. That is Rule A again, so the series alternates A, B, A, B, …
Step 4 is therefore Rule B, applied to LETADS: the end letters L and S exchange, putting S in slot 1 and L in slot 6; the middle block E, T, A, D rotates one place right to D, E, T, A. Reading slots 1 to 6 gives S, D, E, T, A, L.
Result. The fifth term of the pattern is SDETAL.
Cross-check. Run the alternation forward from the first term and every printed term must reappear: SLATED —Rule A→ ALSDET —Rule B→ TELSDA —Rule A→ LETADS —Rule B→ SDETAL. The same pair of rules reproduces all four given terms, not just one step. SDETAL also uses each letter of SLATED exactly once, as every term of this series must.
Contrast. Each of the other arrangements comes from LETADS by a different operation:
Arrangement | Operation on LETADS that produces it |
|---|---|
S T E D A L | Ends exchanged, but the middle block’s letters exchanged in pairs (E with T, A with D) instead of rotated. |
S L E T A D | The whole six-letter term rotated one place to the right, with no exchange of the end letters. |
S D A T E L | The whole six-letter term reversed. |