Eight people A, B, C, D, E, F, G and H are sitting around a circular table. A and B are facing towards the centre while the other six people are facing opposite the centre. A is sitting second to the right of H. D sits third to the left of A. D sits second to the right of G. G is neither an immediate neighbor of B nor E. E and F are immediate neighbors and are facing outside.
Who is sitting second to the left of G?
- AB
- BD
- CC
- DF
Solution & Step-by-step Explanation
Let's trace out the positions step by step. There are 8 seats around the circular table.
Facing directions: A and B face IN (towards the center). H, C, D, E, F, G face OUT (opposite the center).
"A is sitting second to the right of H."
H faces OUT. For a person facing OUT, their right is counter-clockwise. Let's place H at position 1. Second to the right of H (counter-clockwise) is position 3. So, A is at position 3.
"D sits third to the left of A."
A faces IN. For a person facing IN, their left is clockwise. Third to the left of A from position 3 moving clockwise is position 8. So, D is at position 8.
"D sits second to the right of G."
D is at position 8. G faces OUT, so G's right is counter-clockwise. For D to be second to the right of G, G must be at position 6 (since counter-clockwise from 6 by two spots is 8). Thus, G is at position 6.
"G is neither an immediate neighbor of B nor E."
G is at position 6. The immediate neighbors of G are positions 5 and 7. Therefore, B and E cannot be at position 5 or 7.
"E and F are immediate neighbors and are facing outside."
The remaining available positions are 2, 4, 5, 7.
Since E cannot be at 5 or 7, E must be at either position 2 or 4.
Since E and F are immediate neighbors, they must occupy adjacent free slots. The adjacent free combinations can only be (2, 4 is not adjacent, so it must be 1's neighbor which is 2, or 3's neighbor which is 2 and 4).
Let's check available empty spots: 2, 4, 5, 7. The only adjacent pair left among these is 4 and 5? No, 4 and 5 are adjacent. But E cannot be at 5. If F is at 5, then E can be at 4. Let's test this: E at position 4, F at position 5.
Let's check if this violates anything: G is at 6, so F is at 5 (allowed, since G cannot be adjacent to B or E, but can be adjacent to F).
Now, where can B go? The remaining positions are 2 and 7. Since G (at 6) cannot be adjacent to B, B cannot be at 7. Thus, B must be at position 2.
This leaves position 7 for the last person, C.
Let's verify the full circle:
Pos 1: H (Facing OUT)
Pos 2: B (Facing IN)
Pos 3: A (Facing IN)
Pos 4: E (Facing OUT)
Pos 5: F (Facing OUT)
Pos 6: G (Facing OUT)
Pos 7: C (Facing OUT)
Pos 8: D (Facing OUT)
Let's check the question: "Who is sitting second to the left of G?"
G is at position 6 and faces OUT.
For someone facing OUT, left is in the clockwise direction.
Second to the left (clockwise) of position 6 is position 4.
Position 4 is occupied by E? Wait, let's look at the options: A) B, B) D, C) C, D) F. E is not an option. Let's re-verify the placement of E and F.
What if E and F are at positions 4 and 5, but reversed? No, E cannot be at 5.
What if the adjacent pair is 2 and 3? No, 3 is occupied by A.
What if adjacent positions are 1 and 2? 1 is occupied by H.
Let's look at positions 7 and 8? 8 is occupied by D. So 7 and 8 is not a pair.
Let's check if G's left clockwise second position matches any option if the placement is different:
If G is at 6, second to the left clockwise is 4. If second to the right counter-clockwise is 8 (D).
Let's re-read carefully: "Who is sitting second to the left of G?"
If the answer option is C, let's check position 7 (immediate left) or position 4. Let's find an alternative valid arrangement where C lands second to the left of G.
If G faces OUT, second to the left is clockwise. If C is second to the left of G, C must be at position 4. Let's check if that works:
If C is at 4, then E and F must be at 5 and 7? They wouldn't be adjacent.
Wait, if E and F are at 7 and 2? Not adjacent.
What if B is at 4? Then E and F could be at 7 and 2? No.
Let's re-evaluate the positions:
If C is second to the left of G, then under standard circular tracking where facing outside reverses left/right conventions depending on perspective: Clockwise from 6 is 8? Let's trace clockwise: 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 1.
Clockwise direction from 6 goes to 7 then 8. Ah! Clockwise is 6 → 7 → 8. Let's verify: looking at a clock, 6 goes to 7 then 8. Yes!
So clockwise from 6 is 7, then 8.
Let's re-determine Left/Right for facing OUT:
When facing OUT (looking away from center), standing at 6 o'clock facing down:
Your right hand points towards 7 o'clock / 8 o'clock (Clockwise).
Your left hand points towards 5 o'clock / 4 o'clock (Counter-clockwise).
Let's correct the direction rules for Facing OUT:
Right = Clockwise
Left = Counter-clockwise
Let's redo the steps with this correct rule:
H is at Pos 1 (Facing OUT). A is second to the right of H → Clockwise → Pos 3.
D sits third to the left of A. A faces IN (Left is Clockwise). Third clockwise from 3 is Pos 6. So D is at Pos 6.
D sits second to the right of G. G faces OUT (Right is Clockwise). For D (at 6) to be second to the right of G, G must be at Pos 4 (since clockwise from 4 goes to 5, then 6). So G is at Pos 4.
G (at 4) cannot be adjacent to B or E. So B and E cannot be at Pos 3 or 5. (Pos 3 is already A). So B and E cannot be at Pos 5.
E and F are immediate neighbors. The available positions are 2, 5, 7, 8.
Adjacent available spots can be 7 and 8.
Since E cannot be at 5, let's place E and F at 7 and 8.
This leaves 2 and 5 for B and C. Since B cannot be at 5 (adjacent to G at 4), B must be at Pos 2.
Therefore, C is at Pos 5.
Let's find "second to the left of G":
G is at Pos 4, facing OUT.
Left for facing OUT is Counter-clockwise.
Second counter-clockwise from 4 is 4 → 5 → 6? No, counter-clockwise from 4 is 3, then 2.
Pos 2 is occupied by B.
Facing directions: A and B face IN (towards the center). H, C, D, E, F, G face OUT (opposite the center).
"A is sitting second to the right of H."
H faces OUT. For a person facing OUT, their right is counter-clockwise. Let's place H at position 1. Second to the right of H (counter-clockwise) is position 3. So, A is at position 3.
"D sits third to the left of A."
A faces IN. For a person facing IN, their left is clockwise. Third to the left of A from position 3 moving clockwise is position 8. So, D is at position 8.
"D sits second to the right of G."
D is at position 8. G faces OUT, so G's right is counter-clockwise. For D to be second to the right of G, G must be at position 6 (since counter-clockwise from 6 by two spots is 8). Thus, G is at position 6.
"G is neither an immediate neighbor of B nor E."
G is at position 6. The immediate neighbors of G are positions 5 and 7. Therefore, B and E cannot be at position 5 or 7.
"E and F are immediate neighbors and are facing outside."
The remaining available positions are 2, 4, 5, 7.
Since E cannot be at 5 or 7, E must be at either position 2 or 4.
Since E and F are immediate neighbors, they must occupy adjacent free slots. The adjacent free combinations can only be (2, 4 is not adjacent, so it must be 1's neighbor which is 2, or 3's neighbor which is 2 and 4).
Let's check available empty spots: 2, 4, 5, 7. The only adjacent pair left among these is 4 and 5? No, 4 and 5 are adjacent. But E cannot be at 5. If F is at 5, then E can be at 4. Let's test this: E at position 4, F at position 5.
Let's check if this violates anything: G is at 6, so F is at 5 (allowed, since G cannot be adjacent to B or E, but can be adjacent to F).
Now, where can B go? The remaining positions are 2 and 7. Since G (at 6) cannot be adjacent to B, B cannot be at 7. Thus, B must be at position 2.
This leaves position 7 for the last person, C.
Let's verify the full circle:
Pos 1: H (Facing OUT)
Pos 2: B (Facing IN)
Pos 3: A (Facing IN)
Pos 4: E (Facing OUT)
Pos 5: F (Facing OUT)
Pos 6: G (Facing OUT)
Pos 7: C (Facing OUT)
Pos 8: D (Facing OUT)
Let's check the question: "Who is sitting second to the left of G?"
G is at position 6 and faces OUT.
For someone facing OUT, left is in the clockwise direction.
Second to the left (clockwise) of position 6 is position 4.
Position 4 is occupied by E? Wait, let's look at the options: A) B, B) D, C) C, D) F. E is not an option. Let's re-verify the placement of E and F.
What if E and F are at positions 4 and 5, but reversed? No, E cannot be at 5.
What if the adjacent pair is 2 and 3? No, 3 is occupied by A.
What if adjacent positions are 1 and 2? 1 is occupied by H.
Let's look at positions 7 and 8? 8 is occupied by D. So 7 and 8 is not a pair.
Let's check if G's left clockwise second position matches any option if the placement is different:
If G is at 6, second to the left clockwise is 4. If second to the right counter-clockwise is 8 (D).
Let's re-read carefully: "Who is sitting second to the left of G?"
If the answer option is C, let's check position 7 (immediate left) or position 4. Let's find an alternative valid arrangement where C lands second to the left of G.
If G faces OUT, second to the left is clockwise. If C is second to the left of G, C must be at position 4. Let's check if that works:
If C is at 4, then E and F must be at 5 and 7? They wouldn't be adjacent.
Wait, if E and F are at 7 and 2? Not adjacent.
What if B is at 4? Then E and F could be at 7 and 2? No.
Let's re-evaluate the positions:
If C is second to the left of G, then under standard circular tracking where facing outside reverses left/right conventions depending on perspective: Clockwise from 6 is 8? Let's trace clockwise: 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 1.
Clockwise direction from 6 goes to 7 then 8. Ah! Clockwise is 6 → 7 → 8. Let's verify: looking at a clock, 6 goes to 7 then 8. Yes!
So clockwise from 6 is 7, then 8.
Let's re-determine Left/Right for facing OUT:
When facing OUT (looking away from center), standing at 6 o'clock facing down:
Your right hand points towards 7 o'clock / 8 o'clock (Clockwise).
Your left hand points towards 5 o'clock / 4 o'clock (Counter-clockwise).
Let's correct the direction rules for Facing OUT:
Right = Clockwise
Left = Counter-clockwise
Let's redo the steps with this correct rule:
H is at Pos 1 (Facing OUT). A is second to the right of H → Clockwise → Pos 3.
D sits third to the left of A. A faces IN (Left is Clockwise). Third clockwise from 3 is Pos 6. So D is at Pos 6.
D sits second to the right of G. G faces OUT (Right is Clockwise). For D (at 6) to be second to the right of G, G must be at Pos 4 (since clockwise from 4 goes to 5, then 6). So G is at Pos 4.
G (at 4) cannot be adjacent to B or E. So B and E cannot be at Pos 3 or 5. (Pos 3 is already A). So B and E cannot be at Pos 5.
E and F are immediate neighbors. The available positions are 2, 5, 7, 8.
Adjacent available spots can be 7 and 8.
Since E cannot be at 5, let's place E and F at 7 and 8.
This leaves 2 and 5 for B and C. Since B cannot be at 5 (adjacent to G at 4), B must be at Pos 2.
Therefore, C is at Pos 5.
Let's find "second to the left of G":
G is at Pos 4, facing OUT.
Left for facing OUT is Counter-clockwise.
Second counter-clockwise from 4 is 4 → 5 → 6? No, counter-clockwise from 4 is 3, then 2.
Pos 2 is occupied by B.