Seven friends are sitting in a straight line facing North - A, B, C, D, E, F,…
2025
Seven friends are sitting in a straight line facing North - A, B, C, D, E, F, and G. B is third to the left of E, who is at one of the ends. D is second to the right of F. Who is sitting in the middle?
- A.
A
- B.
B
- C.
C
- D.
D
Show answer & explanation
Correct answer: B
Concept: In a straight-line seating arrangement, the phrase "Xth to the left of Y" fixes a seat number equal to position(Y) minus X, counting seats 1 to n from the left end. When Y is additionally said to sit "at one of the ends," only the end for which this subtraction stays within 1 to n is actually possible - the other end gives a seat number outside the row and is ruled out. For an odd row of n = 7 seats, the middle seat is always seat number 4, counted from either end.
Application:
Number the seven seats 1 (left end) to 7 (right end).
The clue "B is third to the left of E" gives position(B) = position(E) - 3.
E sits at one end, so position(E) is either 1 or 7.
If position(E) = 1, then position(B) = 1 - 3 = -2, which is not a valid seat, so this case is impossible.
So position(E) = 7 (the right end), which gives position(B) = 7 - 3 = 4 - exactly the middle seat of the row.
The second clue, "D is second to the right of F," only fixes F and D among the remaining seats {1, 2, 3, 5, 6} (for example F at 1 and D at 3, or F at 3 and D at 5); it never touches seat 4, which is already fixed.
Cross-check: Testing the other possible end for E confirms this - placing E at the left end leaves no seat three places to its left, so that branch fails immediately. E at the right end is therefore the only arrangement consistent with the clue, and with it, B's seat is fixed as the middle seat regardless of how A, C, F and G are eventually seated around it.
Result: B is sitting in the middle.