Eleven students A, B, C, D, E, F, G, H, I, J and K are sitting in a row of the…

2024

Eleven students A, B, C, D, E, F, G, H, I, J and K are sitting in a row of the class facing the teacher. D, who is to the immediate left of F, is second to the right of C. A is second to the right of E, who is at one of the ends. J is the immediate neighbor of A and B and third to the left of G. H is to the immediate left of D and third to the right of I.

Which of the following groups of friends is sitting to the right of G?

  1. A.

    IBJA

  2. B.

    ICHDF

  3. C.

    CHDF

  4. D.

    CHDE

Attempted by 9 students.

Show answer & explanation

Correct answer: C

Concept: In a linear row-arrangement puzzle, translate each relational clue into a short positional code — “second to the right” means exactly two seats away in that direction, “immediate left/right” means adjacent seats — then chain any codes that share a common person into one continuous block. The unique valid arrangement is whichever placement of these blocks exactly fills the fixed seat count (11 here) without leaving a gap or running over.

  1. D is immediately to the left of F, and D is two seats to the right of C — chain these into the block C _ D F (C, an empty seat, D, then F).

  2. A is two seats to the right of E, and E sits at one end. If E took the right end, no seat would remain two places to its right for A, so E must sit at the left end, giving E _ A across seats 1–3.

  3. J is the immediate neighbour of both A and B, and is three seats to the left of G. Seat 2 (between E and A) has room for only one neighbour, so J cannot sit there; J must instead sit right after A, at seat 4, with B on its other side at seat 5. Being three seats to the left of G then places G four seats after J, at seat 7, so E _ A J B _ G occupies seats 1–7.

  4. H is immediately to the left of D, and H is three seats to the right of I — combined with the C _ D F block above, this gives the six-seat block I _ C H D F, with H sitting between C and D.

  5. The chain E _ A J B _ G fixes positions 1, 3, 4, 5, and 7 to E, A, J, B, and G, leaving two blanks inside it (seats 2 and 6) and four completely open seats after it (seats 8-11). The six-seat block I _ C H D F cannot fit only within seats 8-11 (just four seats) or start any later without overflowing past seat 11, so it must start at seat 6: its first seat (I) fills the blank at seat 6, its second seat coincides with the already-fixed seat 7 (G) — consistent, since that block position was never assigned its own letter — and its last four seats (C, H, D, F) fill the previously-open seats 8-11.

  6. The one student left unplaced, K, takes the only seat still empty — seat 2, between E and A.

This gives the full row (seat 1 to seat 11): E, K, A, J, B, I, G, C, H, D, F.

Cross-check: each clue holds in this row:

  • D (seat 10) sits immediately left of F (seat 11), and two seats right of C (seat 8).

  • A (seat 3) sits two seats right of E (seat 1), which is the left end of the row.

  • J (seat 4) sits between A (seat 3) and B (seat 5), and three seats left of G (seat 7).

  • H (seat 9) sits immediately left of D (seat 10), and three seats right of I (seat 6).

Result: G sits at seat 7, so the four seats to G's right — seats 8 through 11 — hold C, H, D, and F, in that order. The group of friends seated to the right of G is C, H, D, F.

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