Study the following information carefully to answer the given questions:
Eight persons- A, B, C, D, E, F, G, and H sit around a square table such that four Persons face inside and sit middle of the table. Four faces outside and sit corner of the table.
G sits second left of C. Three person sits between D and B. H sits opposite A but does not sit at the middle of the table. D sits 2nd left of A. F sits second to the right of C. E sits immediate right of B.
How many persons sit between G and F?
Correct Answer :
Three
Solution :
Correct Option: Three
Let's analyze the given statements step-by-step to determine the seating arrangement of the eight persons (A, B, C, D, E, F, G, and H) around the square table:
1. Table Setup:
- 4 persons sit at the middle of the sides and face inside (towards the center).
- 4 persons sit at the corners and face outside (away from the center).
2. Placing H and A:
- "H sits opposite A but does not sit at the middle of the table."
This means H sits at one of the corners and faces outside. Since H sits opposite A, A must also sit at a corner opposite to H, facing outside.
3. Placing D:
- "D sits 2nd left of A."
Since A is at a corner facing outside, moving to the left of A means moving clockwise around the table. Thus, D sits at the middle of the side, 2 positions clockwise from A. Since D is in the middle of a side, D faces inside.
4. Placing B:
- "Three person sits between D and B."
In an 8-person circular/square table, having 3 persons between two people means they sit directly opposite each other. Since D sits at the middle of a side facing inside, B must sit at the opposite middle of the side, facing inside.
5. Placing E:
- "E sits immediate right of B."
Since B sits in the middle of a side and faces inside, the immediate right of B is the corner counter-clockwise to B. Therefore, E sits at a corner facing outside.
6. Placing C, G, and F:
- "F sits second to the right of C."
- "G sits second left of C."
Let's find the remaining spots. The spots already filled are H (corner), A (corner), B (middle), D (middle), E (corner).
The remaining spots are:
- 1 corner (opposite E)
- 2 middle positions (the two sides adjacent to H and A)
Since C must have both a second-right spot (F) and a second-left spot (G), C must be seated at the remaining middle position on one side. If C is in the middle facing inside:
- Immediate left/right are corners, so second to the left and second to the right are middle positions.
Placing C at the remaining middle position facing inside:
- Right of C (counter-clockwise) 2nd spot is occupied by D or B depending on orientation.
Checking positions precisely:
- Let H be at top-left corner (facing outside).
- Then A is at bottom-right corner (facing outside).
- D sits 2nd left of A (clockwise) -> D is at bottom-middle (facing inside).
- B is opposite D -> B is at top-middle (facing inside).
- E sits immediate right of B (facing inside, right is top-left/top-right? For facing inside, right is counter-clockwise -> top-right corner). So E is at top-right corner.
- The remaining positions are: bottom-left corner, left-middle, right-middle.
- If C sits at left-middle (facing inside):
- 2nd right of C (counter-clockwise) is top-middle (B - occupied, wait!). If C faces inside, right is counter-clockwise, 2nd right is bottom-middle (D - occupied!).
- Therefore, C must sit at right-middle (facing inside):
- Facing inside, right is counter-clockwise -> 2nd right of C is top-middle (B? No, from right-middle, counter-clockwise goes to top-right corner then top-middle, so 2nd position is top-middle, but wait!).
Let's recount positions around the table in order (clockwise):
1. Top-left corner (H, facing outside)
2. Top-middle (B, facing inside)
3. Top-right corner (E, facing outside)
4. Right-middle (C, facing inside)
5. Bottom-right corner (A, facing outside)
6. Bottom-middle (D, facing inside)
7. Bottom-left corner (G or F)
8. Left-middle (F or G)
Let's verify C at Right-middle (facing inside):
- Right of C (counter-clockwise): 1st right is E (top-right corner), 2nd right is B (top-middle). But B is already there. So C cannot be at right-middle facing inside if 2nd right is B.
- Let's check left of A (facing outside):
A is at bottom-right (facing outside). Left of A is clockwise -> bottom-middle (D). Correct!
So 2nd left of A is bottom-middle (D). Wait, 1st left of A is bottom-middle? No, 1st position clockwise from bottom-right corner is bottom-middle (D). So D is 1st left of A? The prompt says "D sits 2nd left of A".
Ah! If A is at bottom-right corner (facing outside), its left direction is clockwise (towards bottom-left corner).
- 1st left of A = bottom-left corner.
- 2nd left of A = left-middle! So D is at left-middle (facing inside).
- Then B (opposite D) is at right-middle (facing inside).
- E is immediate right of B (facing inside, right is counter-clockwise -> top-right corner). So E is at top-right corner.
- H is opposite A -> H is at top-left corner.
- Now remaining middle positions are: top-middle and bottom-middle.
- Let C be at bottom-middle (facing inside):
- Facing inside: Left is clockwise (towards bottom-left corner), Right is counter-clockwise (towards bottom-right corner).
- 2nd right of C (counter-clockwise): 1st right is bottom-right corner (A), 2nd right is right-middle (B). Wait, B is at right-middle! Let's check if 2nd right is available.
- What if C is at top-middle (facing inside)?
- Facing inside: Right is counter-clockwise (towards top-left corner H). 1st right = top-left (H), 2nd right = left-middle (D). Still occupied!
- What if D is 2nd left of A going counter-clockwise? For facing outside, left is clockwise. 1st left = corner/side.
Let's list the 8 positions in clockwise order around the square table:
P1: Top-Left (Corner, Outside)
P2: Top-Middle (Side, Inside)
P3: Top-Right (Corner, Outside)
P4: Right-Middle (Side, Inside)
P5: Bottom-Right (Corner, Outside)
P6: Bottom-Middle (Side, Inside)
P7: Bottom-Left (Corner, Outside)
P8: Left-Middle (Side, Inside)
- H and A are opposite corners: H at P1, A at P5.
- A is at P5 (facing outside). Facing outside means Left = Clockwise (P6, P7...), Right = Counter-clockwise (P4, P3...).
- D sits 2nd left of A -> 2nd clockwise from P5 is P7 (Bottom-Left Corner). But D is in the middle of a side! Wait, P7 is a corner. P6 is Bottom-Middle (1 step), P7 is Bottom-Left (2 steps).
- If D is at P8 (Left-Middle): distance from P5 to P8 is 3 steps.
- If D sits 2nd left of A, it means there is 1 person between A and D. So P5 to P7 has 1 person at P6. Thus D is at P7? But D faces inside (middle of side). So D must be at P6 or P8 or P2 or P4.
- If 2nd left means 2 positions away (i.e. index + 2):
If D is at P6 (Bottom-Middle, 1 step) or P8... Wait! In many seating arrangement puzzles, "2nd to the left" means 2nd position (1 person in between). If corners and sides alternate: 1st position from a corner is a side, 2nd position is a corner. So 2nd left of a corner would be a corner!
Unless the seating arrangement counts only relative positions! But here 8 positions are fixed.
Let's re-verify: "D sits 2nd left of A." If A is at P5 (corner, facing outside), 2nd left is P7 (corner). But D sits at middle of table? Wait, the problem says "H does not sit at the middle", it doesn't explicitly restrict D, but it says "four Persons face inside and sit middle of the table. Four faces outside and sit corner of the table."
If D is 2nd left of A, and D is at middle of the table (say P6), then A must be at P8 (Left-Middle) or P4? But A is at a corner!
If A is at P5 (corner, outside), left is P6 (side, inside). So 2nd left could mean P7 (corner) or if counting side positions, P8.
Regardless of the exact diagram orientation, G and F are placed relative to C:
- G is 2nd to the left of C.
- F is 2nd to the right of C.
This places C exactly in the middle between G and F!
7. Finding persons between G and F:
Since G is 2nd to the left of C and F is 2nd to the right of C in an 8-person circular table:
- Moving from G to F in one direction: G -> (1 person) -> C -> (1 person) -> F.
- Thus, counting from one side, there are 3 persons (the person between G and C, C itself, and the person between C and F) between G and F.
- Counting from the other side around the 8-person table: 8 - 2 (G and F) - 3 = 3 persons.
Therefore, no matter which direction you count around the table, exactly 3 persons sit between G and F.
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