Six friends — A, B, C, D, E, F — sit in a row facing north. B is to the immediate left of D. A sits at one end. C is third to the right of A. E is not next to B. F is somewhere to the left of C.
SOLUTION....
(a) Six friends — A, B, C, D, E, F — sitting in a row facing north
Given facts (interpreted literally with left/right on the page):
B is immediately to the left of D.
A sits at one end.
C is third to the right of A.
E is not next to B.
F is somewhere to the left of C.
Reasoning:
Let the seats be positions 1 → 6 left-to-right on the page.
A must be at an end. If A were at position 6, there is no room for “third to the right” of A, so A must be at the left end (position 1).
“C is third to the right of A” → from position 1, C is at position 4. So now:
F must be somewhere left of C → F must be in position 2 or 3.
B is immediately left of D (they occupy two adjacent seats with B left and D right). The adjacent pair B–D can only occupy positions (2,3) or (5,6).
E cannot be next to B, so we must place B–D and E so E is not adjacent to B.
Two valid arrangements arise (both satisfy every condition):
Arrangement 1 (F at pos2):
Positions:A, F, E, C, B, D
(pos1 A; pos2 F; pos3 E; pos4 C; pos5 B; pos6 D)
Here B and D are adjacent (pos5,6), F is left of C, and E is not next to B.Arrangement 2 (F at pos3):
Positions:A, E, F, C, B, D
(pos1 A; pos2 E; pos3 F; pos4 C; pos5 B; pos6 D)
Again all conditions hold.
So the puzzle admits two correct seatings:
A — F — E — C — B — D
A — E — F — C — B — D
(Left → Right, all facing north.)