Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west.…
2014
Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west. B and F are not sitting on either of the edges; G is sitting to the left of D and H is sitting to the right of J; There are four persons between E and A; I is to the north of B and F is to the South of D; J sits immediately between A and D (adjacent to both, with no one else between) and G sits immediately between E and F (adjacent to both, with no one else between). There are two persons between H and C.
Who among the following is definitely sitting at one of the ends?
- A.
C
- B.
H
- C.
E
- D.
None of these
Attempted by 11 students.
Show answer & explanation
Correct answer: C
CONCEPT: In a linear seating puzzle, first lock any pair fixed by an exact numeric gap ("four persons between X and Y" means their seats are exactly 5 apart), then chain the remaining relative-order and immediate-"between" clues onto that pair. If two or more arrangements satisfy every clue, only the seat that is IDENTICAL in every valid arrangement is "definitely" true — a seat that differs between arrangements is not.
APPLICATION: Since all ten students face the same direction (west), their own right side points north and their own left side points south, so every "left of/right of" clue and every "north of/south of" clue can be placed on one single, consistent order.
"Four persons between E and A" fixes E and A exactly 5 seats apart on the row of 10.
"G is between E and F" (immediately, no one else between) combined with "G is to the left of D" and "F is to the south of D" places the E–G–F block right next to D, on D's near side.
"J is between A and D" (immediately) places J right next to both A and D, giving a fixed six-seat chain E–G–F–D–J–A running from one end of the row inward.
Testing this six-seat chain against the 10 seats and the edge rule ("B and F are not on either edge") pins E at one end of the row, with G, F, D, J, A occupying the next five seats in order.
The four seats left over (for B, C, H and I) must satisfy "I is to the north of B" and "H is to the right of J", which places B then I next to A's side, leaving the outermost of the four remaining seats for H or C — and "there are two persons between H and C" (exactly 3 seats apart) holds equally whichever of H or C takes that outer seat.
So exactly two seatings satisfy every single clue — they differ only in whether H or C sits at the far end:
Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 | Seat 6 | Seat 7 | Seat 8 | Seat 9 | Seat 10 |
|---|---|---|---|---|---|---|---|---|---|
H | I | B | C | A | J | D | F | G | E |
C | I | B | H | A | J | D | F | G | E |
CROSS-CHECK: Both rows above satisfy every clue (edge rule, the E–A gap, the H–C gap, and every left/right and north/south relation) — check any one clue against both rows and it holds in each. The two rows differ only in Seat 1 vs Seat 4 (H and C swap places); every other seat, including Seat 10, is identical in both.
RESULT: E occupies Seat 10 — an end of the row — in both valid seatings, so E is definitely sitting at one of the ends. H sits at an end only in the first seating and C sits at an end only in the second, so neither H nor C is definite, and since E does satisfy the condition, "None of these" is wrong.