Seating Arrangement - Expert Level: parallel rows EXPERT

Comprehensive self assessment worksheet covering 20 expert-level seating arrangement problems. Worksheet 28 of 30 emphasizes parallel rows. Master facing directions, adjacent seating, opposite positions through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

πŸ“ Worksheet 28 of 30 β€’ 20 questions β€’ ⏱️ Estimated time: 20 minutes β€’ 🎯 Expert level

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Worksheet 28 of 30 (93% complete)

Question 1

Six persons P, Q, U, T, R and S are sitting in a row. Some are facing North and some are facing South. P sits third from the left end facing North. Q sits second to the right of P and faces opposite direction. U sits at the left extreme end facing South. T sits immediately to the left of Q facing North. S sits at the right extreme end. Who sits between U and P?
Solution Approach:

Step 1: Mark directions
↑ = North facing, ↓ = South facing

Step 2: Apply position-based conditions
- P sits third from the left end facing North (↑) β†’ Position 3
- U sits at the left extreme end facing South (↓) β†’ Position 1

Position: U(↓) _ P(↑) _ _ _

Step 3: Apply relative positioning
- Q sits second to the right of P (pos 3) β†’ Position 5
- Q faces opposite direction to P (North) β†’ Q faces South (↓)
- T sits immediately to the left of Q (pos 5) facing North (↑) β†’ Position 4

Position: U(↓) _ P(↑) T(↑) Q(↓) _

Step 4: Fill remaining positions
Remaining persons: R, S
Position 2 gets R, Position 6 gets S

Final Arrangement:
Pos: U(↓) R(↑) P(↑) T(↑) Q(↓) S(↑)

Verification:
βœ“ P at pos 3, facing North
βœ“ Q at pos 5 (second right of P), facing South (opposite of P)
βœ“ U at pos 1 (left extreme), facing South
βœ“ T at pos 4 (immediately left of Q), facing North

Person between U (pos 1) and P (pos 3): pos 2 = R

Answer: R sits between U and P.

Question 2

Six persons P, O, M, K, N and L sit around a circular table facing outward. O sits second to the left of P. M sits opposite to O. K sits immediately to the right of M. N sits opposite to P. Who sits immediately to the left of O?
Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- O sits second to the LEFT of P: left(outward)=CW, so O is 2 CW from P.
pos[O] = 3
- M sits opposite O (pos 3): pos 6
- K sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW β†’ pos 5
- N sits opposite P (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:P β†’ pos2:L β†’ pos3:O β†’ pos4:N β†’ pos5:K β†’ pos6:M
(All facing outward β†—)

Find immediate left of O (pos 3):
Left (outward) = clockwise β†’ pos 4 = N

Verification:
βœ“ O second to left of P (CW direction)
βœ“ M opposite O
βœ“ K immediately right (anti-CW) of M
βœ“ N opposite P

Answer: N sits immediately to the left of O.

Question 3

Six persons P, N, O, M, K and L sit around a circular table facing outward. N sits second to the left of P. O sits opposite to N. M sits immediately to the right of O. K sits opposite to P. Who sits immediately to the left of N?
Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- N sits second to the LEFT of P: left(outward)=CW, so N is 2 CW from P.
pos[N] = 3
- O sits opposite N (pos 3): pos 6
- M sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW β†’ pos 5
- K sits opposite P (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:P β†’ pos2:L β†’ pos3:N β†’ pos4:K β†’ pos5:M β†’ pos6:O
(All facing outward β†—)

Find immediate left of N (pos 3):
Left (outward) = clockwise β†’ pos 4 = K

Verification:
βœ“ N second to left of P (CW direction)
βœ“ O opposite N
βœ“ M immediately right (anti-CW) of O
βœ“ K opposite P

Answer: K sits immediately to the left of N.

Question 4

Six persons C, F, D, B, A and E are sitting around a circular table facing the center. C sits second to the left of F. D sits opposite to C. B sits immediately to the right of D. E is not adjacent to B. Who sits opposite to F?
Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix C at position 1 (reference point)
- C is second to the LEFT of F β†’ F is 2 clockwise from C
pos[F] = 3
- D sits OPPOSITE C (pos 1) β†’ pos 4
- B sits immediately to the right of D (pos 4) β†’ pos 5

Step 3: Resolve remaining positions
Remaining persons: E, A β†’ remaining seats: [2, 6]
E is NOT adjacent to B (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore E β†’ pos 2, and A β†’ pos 6.

Final Arrangement (clockwise):
pos1:C β†’ pos2:E β†’ pos3:F β†’ pos4:D β†’ pos5:B β†’ pos6:A
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

F is at pos 3 β†’ opposite = pos 6 = A

Answer: A sits opposite to F.

Question 5

There are 10 seats in a row, all facing North. 8 persons F, B, H, C, D, G, A and E are seated, leaving 2 seats empty. F sits at seat 3. E sits at seat 8. One empty seat is at an extreme end. B sits immediately to the right of an empty seat. C sits fourth to the left of E. How many persons sit between the two empty seats?
Solution Approach:

Step 1: Mark total positions
Seats: 1 2 3 4 5 6 7 8 9 10
Total: 10 seats, 8 persons, 2 empty.

Step 2: Place definite positions
- F at seat 3
- E at seat 8 (seat 8)
- One empty seat at extreme end β†’ seat 1 is empty

Seat: 1(_) 2(_) 3(F) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

Step 3: Apply empty seat adjacency
- B sits immediately to the RIGHT of an empty seat
- Empty at seat 1 β†’ seat 2 = B βœ“

Seat: 1(_) 2(B) 3(F) 4(_) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

Step 4: Apply "fourth to the left" condition
- C sits fourth to the LEFT of E (seat 8)
- Fourth to left: 8 β†’ 7 β†’ 6 β†’ 5 β†’ 4
- C at seat 4 βœ“

Seat: 1(_) 2(B) 3(F) 4(C) 5(_) 6(_) 7(_) 8(E) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: D, G, A, H β†’ fill seats 5, 6, 7, 9, 10 minus one empty.
After placing D(5), G(6), A(7), H(10): seat 9 is empty.

Step 6: Final arrangement
Seat: 1(_) 2(B) 3(F) 4(C) 5(D) 6(G) 7(A) 8(E) 9(_) 10(H)

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: B, F, C, D, G, A, E = 7 persons

Verification:
βœ“ F at seat 3
βœ“ E at seat 8
βœ“ Empty at seat 1 (extreme end)
βœ“ B immediately right of empty seat 1
βœ“ C fourth to left of E (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

Question 6

Five friends S, T, R, P and Q are sitting in a row facing South. S sits at the right extreme end. T sits second to the right of R. Q sits immediately to the right of R (from viewer's perspective). P is not adjacent to S. Who sits at the left extreme end?
Solution Approach:

Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) β€” "right" in the question = lower position number
- Viewer's "right" (higher position) = person's left side

Step 2: Set up diagram (viewer's perspective)
Position: 1(left) 2 3 4 5(right)

Step 3: Apply conditions
- S at the right extreme end β†’ Position 5
- T sits second to the right of R:
South-facing right = viewer's left = lower position: pos[T] = pos[R] - 2
Possible: R=3β†’T=1, or R=4β†’T=2
- Q sits immediately to the right of R (viewer's right = higher pos): pos[Q] = pos[R] + 1
If R=3 β†’ Q=4 βœ“ (pos 4 free)
If R=4 β†’ Q=5 = S βœ— (conflict)
∴ R=3, T=1, Q=4

Position: T _ R Q S

Step 4: Apply constraint
- P not adjacent to S (pos 5): P β‰  pos 4 (taken by Q) β†’ P at pos 2 βœ“

Final Arrangement (all facing South ↓):
Position: T P R Q S

Verification:
βœ“ S at right extreme end (pos 5)
βœ“ T second to right of R: pos[T](=1)-2 = 3 = pos[R] (south-facing right=lower)
βœ“ Q immediately right of R (viewer right): pos 3+1 = 4
βœ“ P not adjacent to S (pos 2, not pos 4)

Answer: T sits at the left extreme end (position 1).

Question 7

Five persons A, E, B, C and D are sitting in a row facing North. A sits at one of the extreme ends. E sits second to the right of A. B sits immediately to the left of E. C is not at any extreme end. Who sits at the other extreme end?
Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- A sits at one extreme end β†’ Place A at position 1
- E sits second to the right of A β†’ E at position 3
- B sits immediately to the left of E β†’ B at position 2

Position: A B E _ _

Step 3: Apply constraint conditions
- C is not at any extreme end β†’ remaining positions are 4 and 5; C cannot be at 5, so C at position 4
- Only D remains β†’ D at position 5

Final Arrangement (all facing North ↑):
Position: A B E C D

Verification:
βœ“ A at extreme end (pos 1)
βœ“ E second to the right of A (pos 3)
βœ“ B immediately to the left of E (pos 2)
βœ“ C not at extreme end (pos 4)

Answer: D sits at the other extreme end (position 5).

Question 8

Five persons B, D, A, E and C are sitting in a row facing North. B sits at one of the extreme ends. D sits second to the right of B. A sits immediately to the left of D. E is not at any extreme end. Who sits at the other extreme end?
Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- B sits at one extreme end β†’ Place B at position 1
- D sits second to the right of B β†’ D at position 3
- A sits immediately to the left of D β†’ A at position 2

Position: B A D _ _

Step 3: Apply constraint conditions
- E is not at any extreme end β†’ remaining positions are 4 and 5; E cannot be at 5, so E at position 4
- Only C remains β†’ C at position 5

Final Arrangement (all facing North ↑):
Position: B A D E C

Verification:
βœ“ B at extreme end (pos 1)
βœ“ D second to the right of B (pos 3)
βœ“ A immediately to the left of D (pos 2)
βœ“ E not at extreme end (pos 4)

Answer: C sits at the other extreme end (position 5).

Question 9

Two parallel rows of chairs. Row 1 has E, D, C, B and A facing South. Row 2 has P, T, R, S and Q facing North. Each person in one row faces exactly one person from the other row. C sits fourth from the left end of Row 1. P faces C. E sits at an extreme end of Row 1. D sits second to the right of E. T sits second to the left of P. R sits at an extreme end of Row 2. Q is not adjacent to P in Row 2. Who faces D?
Solution Approach:

Step 1: Draw the double row setup
Row 1 faces South (↓), Row 2 faces North (↑)
Person at position i in Row 1 faces person at position i in Row 2.

Position: 1 2 3 4 5
Row 1 (↓): _ _ _ _ _
Row 2 (↑): _ _ _ _ _

Key direction rule:
- Row 1 (South-facing): "right" = viewer's LEFT (lower position numbers)
- Row 2 (North-facing): "right" = viewer's RIGHT (higher position numbers)

Step 2: Place Row 1 persons
- C sits 4th from the left end of Row 1 β†’ Row 1, pos 4
- E sits at an extreme end: pos 1 or pos 5
- D sits second to the RIGHT of E (south-facing β†’ lower position):
pos[D] = pos[E] - 2
If E at pos 1 β†’ pos[D] = -1 (invalid βœ—)
If E at pos 5 β†’ pos[D] = 3 βœ“ (pos 3 is free)
∴ E at pos 5, D at pos 3 βœ“

Row 1: _ _ D C E
Remaining B,A at pos 1 and 2 (either order β€” pinned next).

Step 3: Place Row 2 persons
- P faces C (pos 4) β†’ P at Row 2, pos 4
- T sits second to the LEFT of P (north-facing β†’ lower position):
pos[T] = pos[P] - 2 = 2 β†’ T at Row 2 pos 2 βœ“
- R sits at extreme end of Row 2: pos 1 or pos 5
- Q is NOT adjacent to P (pos 4): adjacent = pos 3 and pos 5
So Q β‰  pos 3 and Q β‰  pos 5
Remaining positions for R,S,Q: pos 1, pos 3, pos 5
Q not at pos 3 or pos 5 β†’ Q at pos 1
R at extreme β†’ pos 5 (since pos 1 is Q) βœ“
S fills pos 3 βœ“

Row 2: Q T S P R

Final Arrangement:
Position: 1 2 3 4 5
Row 1 (↓): B/A B/A D C E
Row 2 (↑): Q T S P R

Find who faces D:
D is at Row 1, position 3.
Person at Row 2, position 3 = S

Answer: S faces D.

Question 10

Five persons Z, W, X, V and Y are to be seated in a row facing North. The following conditions apply: - If Z sits at an extreme end, then X must sit immediately next to W - If Z does not sit at an extreme end, then V must sit at an extreme end - Y cannot sit next to Z - W sits second from the left Which of the following must be FALSE?
Solution Approach:

Step 1: Apply the fixed condition
- W sits second from the left β†’ W at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with W at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
β€’ Z W X V Y
β€’ Z W X Y V
β€’ X W Y V Z
β€’ V W Z X Y
β€’ Y W Z X V
β€’ Y W X Z V
(shown up to 6)

Step 3: Test each MCQ option

- "Y sits at position 4": βœ“ Possible in at least one valid arrangement
- "Z sits at position 2": βœ— NEVER possible β†’ must be FALSE
- "Z sits at position 4": βœ“ Possible in at least one valid arrangement
- "V sits at position 5": βœ“ Possible in at least one valid arrangement

Step 4: Conclusion
"Z sits at position 2" is impossible in ALL 7 valid arrangement(s) β€” it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "Z sits at position 2" must be FALSE.

Question 11

Three parallel rows of chairs. Row 1 has D, B, A, C facing South. Row 2 has R, P, S, Q facing North. Row 3 has W, X, Z, Y facing South. Row 2 is between Row 1 and Row 3. Persons in Row 1 face persons in Row 2, and persons in Row 2 face persons in Row 3. D faces R who faces W. B sits to the left of D in Row 1. P faces B and also faces X. S sits second to the right of P in Row 2. Who sits at the right extreme of Row 3?
Solution Approach:

Step 1: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- D faces R who faces W: all three in the SAME vertical column.
Place at position 2:
Row1: _ D _ _
Row2: _ R _ _
Row3: _ W _ _

Step 3: Apply left-right conditions
- B sits to the left of D(pos 2) in Row 1 β†’ B at position 1
Row1: B D _ _

Step 4: Second facing relationship
- P faces B(Row1 pos1) β†’ P at Row2 position 1
- P faces X β†’ X at Row3 position 1
Row1: B D _ _
Row2: P R _ _
Row3: X W _ _

Step 5: Apply relative positioning in Row 2
- S sits second to the right of P(pos1): 1+2=3 β†’ S at Row2 position 3
Row2: P R S _
S faces Row1 pos3 β†’ A at Row1 pos3 βœ“
S faces Row3 pos3 β†’ Z at Row3 pos3 βœ“

Step 6: Fill remaining positions
Remaining: Row1 pos4=C, Row2 pos4=Q, Row3 pos4=Y

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): B D A C
Row 2 (↑): P R S Q
Row 3 (↓): X W Z Y

Right extreme of Row 3 = position 4 = Y

Answer: Y

Question 12

Five friends T, R, Q, S and P are sitting in a row facing South. T sits at the right extreme end. R sits second to the right of Q. P sits immediately to the right of Q (from viewer's perspective). S is not adjacent to T. Who sits at the left extreme end?
Solution Approach:

Step 1: Understanding facing South
When persons face South:
- Their right hand points West (viewer's LEFT) β€” "right" in the question = lower position number
- Viewer's "right" (higher position) = person's left side

Step 2: Set up diagram (viewer's perspective)
Position: 1(left) 2 3 4 5(right)

Step 3: Apply conditions
- T at the right extreme end β†’ Position 5
- R sits second to the right of Q:
South-facing right = viewer's left = lower position: pos[R] = pos[Q] - 2
Possible: Q=3β†’R=1, or Q=4β†’R=2
- P sits immediately to the right of Q (viewer's right = higher pos): pos[P] = pos[Q] + 1
If Q=3 β†’ P=4 βœ“ (pos 4 free)
If Q=4 β†’ P=5 = T βœ— (conflict)
∴ Q=3, R=1, P=4

Position: R _ Q P T

Step 4: Apply constraint
- S not adjacent to T (pos 5): S β‰  pos 4 (taken by P) β†’ S at pos 2 βœ“

Final Arrangement (all facing South ↓):
Position: R S Q P T

Verification:
βœ“ T at right extreme end (pos 5)
βœ“ R second to right of Q: pos[R](=1)-2 = 3 = pos[Q] (south-facing right=lower)
βœ“ P immediately right of Q (viewer right): pos 3+1 = 4
βœ“ S not adjacent to T (pos 2, not pos 4)

Answer: R sits at the left extreme end (position 1).

Question 13

Five persons Z, V, W, X and Y are to be seated in a row facing North. The following conditions apply: - If Z sits at an extreme end, then W must sit immediately next to V - If Z does not sit at an extreme end, then X must sit at an extreme end - Y cannot sit next to Z - V sits second from the left Which of the following must be FALSE?
Solution Approach:

Step 1: Apply the fixed condition
- V sits second from the left β†’ V at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with V at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
β€’ Z V W X Y
β€’ Z V W Y X
β€’ W V Y X Z
β€’ X V Z W Y
β€’ Y V Z W X
β€’ Y V W Z X
(shown up to 6)

Step 3: Test each MCQ option

- "X sits at position 4": βœ“ Possible in at least one valid arrangement
- "Y sits at position 4": βœ“ Possible in at least one valid arrangement
- "X sits at position 5": βœ“ Possible in at least one valid arrangement
- "Z sits at position 2": βœ— NEVER possible β†’ must be FALSE

Step 4: Conclusion
"Z sits at position 2" is impossible in ALL 7 valid arrangement(s) β€” it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "Z sits at position 2" must be FALSE.

Question 14

Eight persons are sitting in two concentric circles. Inner circle: B, A, D and C (4 persons) facing the center. Outer circle: Q, R, P and S (4 persons) facing the center (2 positions in outer circle are empty). Each inner person directly faces one outer seat (4 outer seats occupied, 2 empty). Q faces B. A sits immediately to the right of B in the inner circle. C sits opposite to A in the inner circle. R sits second to the right of P in the outer circle. S sits immediately to the left of an empty seat in the outer circle. Who sits opposite to A in the inner circle?
Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) β€” all occupied.
Outer circle: 6 positions O1–O6 clockwise β€” 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- A sits immediately to the right of B (inner circle, facing center: right=CW)
β†’ B and A are adjacent. Possible: B=I1, A=I2 or B=I2, A=I3, etc.
- C sits opposite to A:
If A=I2, then C=I4. Then B=I1 (left of I2), D=I3 (remaining).
All constraints consistent βœ“.

Inner: I1=B, I2=A, I3=D, I4=C

Step 4: Place outer circle persons
- Q faces B(I1) β†’ Q at O1 βœ“
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- R second to right of P (outer, facing center: right=CW, step 2):
Remaining outer persons: R,P,S at O2, O4, O5.
R=O2 β†’ Q=O4, S=O5 βœ“
R=O4 β†’ Q=O6(empty) βœ—
R=O5 β†’ Q=O1=P βœ—
∴ P=O2, R=O4, S=O5 βœ“
- S(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(R) β€” NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) βœ“.

Step 5: Answer the question
A is at I2. Opposite of I2 = I4 = C.

Final Arrangements:
Inner (CW): I1=B, I2=A, I3=D, I4=C
Outer (CW): O1=Q, O2=P, O3=empty, O4=R, O5=S, O6=empty

Verification:
βœ“ Q faces B (I1↔O1)
βœ“ A immediately right of B (I2 is CW from I1)
βœ“ C opposite A (I4 opposite I2)
βœ“ R second right of P (O4 = O2 + 2 CW)
βœ“ S(O5) immediately left of empty O6

Answer: C sits opposite to A.

Question 15

Eight persons are sitting in two concentric circles. Inner circle: A, D, B and C (4 persons) facing the center. Outer circle: R, S, Q and P (4 persons) facing the center (2 positions in outer circle are empty). Each inner person directly faces one outer seat (4 outer seats occupied, 2 empty). R faces A. D sits immediately to the right of A in the inner circle. C sits opposite to D in the inner circle. S sits second to the right of Q in the outer circle. P sits immediately to the left of an empty seat in the outer circle. Who sits opposite to D in the inner circle?
Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) β€” all occupied.
Outer circle: 6 positions O1–O6 clockwise β€” 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- D sits immediately to the right of A (inner circle, facing center: right=CW)
β†’ A and D are adjacent. Possible: A=I1, D=I2 or A=I2, D=I3, etc.
- C sits opposite to D:
If D=I2, then C=I4. Then A=I1 (left of I2), B=I3 (remaining).
All constraints consistent βœ“.

Inner: I1=A, I2=D, I3=B, I4=C

Step 4: Place outer circle persons
- R faces A(I1) β†’ R at O1 βœ“
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- S second to right of Q (outer, facing center: right=CW, step 2):
Remaining outer persons: S,Q,P at O2, O4, O5.
R=O2 β†’ Q=O4, S=O5 βœ“
R=O4 β†’ Q=O6(empty) βœ—
R=O5 β†’ Q=O1=P βœ—
∴ Q=O2, S=O4, P=O5 βœ“
- P(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(S) β€” NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) βœ“.

Step 5: Answer the question
D is at I2. Opposite of I2 = I4 = C.

Final Arrangements:
Inner (CW): I1=A, I2=D, I3=B, I4=C
Outer (CW): O1=R, O2=Q, O3=empty, O4=S, O5=P, O6=empty

Verification:
βœ“ R faces A (I1↔O1)
βœ“ D immediately right of A (I2 is CW from I1)
βœ“ C opposite D (I4 opposite I2)
βœ“ S second right of Q (O4 = O2 + 2 CW)
βœ“ P(O5) immediately left of empty O6

Answer: C sits opposite to D.

Question 16

Six persons Bhanu, Charu, Deepak, Farhan, Esha and Aman are sitting around a hexagonal table, one at each corner, all facing the center. Bhanu sits opposite to Charu. Deepak sits second to the right of Bhanu. Esha sits second to the right of Aman. Farhan is not adjacent to Bhanu. What is the position of Farhan with respect to Deepak?
Solution Approach:

Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Bhanu at H1 (pos 1).
- Bhanu opposite Charu: opp(pos1) = pos4 β†’ Charu at H4

Step 3: Apply relative positioning
- Deepak second to the right of Bhanu(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ Deepak at H3

- Esha second to the right of Aman:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Bhanu=1, Charu=4, Deepak=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Aman: pos5 is 2 clockwise [solver-verified].
β†’ Aman at pos6, Esha at pos2

Step 4: Apply constraint
- Farhan not adjacent to Bhanu(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Farhan at pos5 (not adjacent) βœ“

Final Arrangement (clockwise):
H1:Bhanu β†’ H2:Esha β†’ H3:Deepak β†’ H4:Charu β†’ H5:Farhan β†’ H6:Aman

Step 5: Find Farhan's position relative to Deepak
Deepak at pos3, Farhan at pos5.
pos5 is 2 clockwise from pos3.

Verification:
βœ“ Bhanu opposite Charu
βœ“ Deepak second to right of Bhanu
βœ“ Esha second to right of Aman
βœ“ Farhan not adjacent to Bhanu

Answer: Farhan sits to the second to the right of Deepak.

Question 17

Eight persons P, N, R, T, Q, S, O and M are sitting around a circular table. Some face the center and some face outward. P faces the center. N faces outward and sits third to the right of P. R sits second to the left of P and faces the same direction as N. T faces the center and sits immediately to the right of R. S sits immediately to the right of P. M sits opposite P. O is not adjacent to N. Who sits second to the right of T?
Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix P (faces center) at position 1 (reference point)
- N faces outward, sits third to the RIGHT of P:
P faces center β†’ right = clockwise
3 CW from pos 1 β†’ pos 4
N = pos 4 βœ“

Step 4: Apply relative positions
- R sits second to the LEFT of P (pos 1):
P faces center β†’ left = anti-clockwise
2 anti-CW from pos 1 β†’ pos 7
R faces same as N β†’ OUTWARD
- T faces center, sits immediately to the RIGHT of R (pos 7):
R faces outward β†’ right = anti-clockwise
1 anti-CW from pos 7 β†’ pos 6

Step 5: Fill remaining persons
- S immediately to the RIGHT of P(pos 1, center→CW): pos 2
- M opposite P(pos 1): pos 5
- O not adjacent to N(pos 4): adj = pos 3 & 5
β†’ O at pos 8, Q at pos 3

Final Arrangement (clockwise):
pos1:P(ctr) | pos2:S(out) | pos3:Q(ctr) | pos4:N(out) | pos5:M(out) | pos6:T(ctr) | pos7:R(out) | pos8:O(ctr)

Find second to the right of T (pos 6, center-facing β†’ CW):
2 CW from pos 6: β†’ pos 8 = O

Verification:
βœ“ N(outward) 3 left of P(center): 3 ACW from pos1 = pos4
βœ“ R 2nd left of P, same direction as N (outward)
βœ“ T(center) immediately right of R(outward, right=ACW)
βœ“ S immediately right (CW) of P
βœ“ M opposite P
βœ“ O not adjacent to N

Answer: O sits second to the right of T.

Question 18

There are 10 seats in a row, all facing North. 8 persons G, A, E, D, B, H, F and C are seated, leaving 2 seats empty. G sits at seat 3. C sits at seat 8. One empty seat is at an extreme end. A sits immediately to the right of an empty seat. D sits fourth to the left of C. How many persons sit between the two empty seats?
Solution Approach:

Step 1: Mark total positions
Seats: 1 2 3 4 5 6 7 8 9 10
Total: 10 seats, 8 persons, 2 empty.

Step 2: Place definite positions
- G at seat 3
- C at seat 8 (seat 8)
- One empty seat at extreme end β†’ seat 1 is empty

Seat: 1(_) 2(_) 3(G) 4(_) 5(_) 6(_) 7(_) 8(C) 9(_) 10(_)

Step 3: Apply empty seat adjacency
- A sits immediately to the RIGHT of an empty seat
- Empty at seat 1 β†’ seat 2 = A βœ“

Seat: 1(_) 2(A) 3(G) 4(_) 5(_) 6(_) 7(_) 8(C) 9(_) 10(_)

Step 4: Apply "fourth to the left" condition
- D sits fourth to the LEFT of C (seat 8)
- Fourth to left: 8 β†’ 7 β†’ 6 β†’ 5 β†’ 4
- D at seat 4 βœ“

Seat: 1(_) 2(A) 3(G) 4(D) 5(_) 6(_) 7(_) 8(C) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: B, H, F, E β†’ fill seats 5, 6, 7, 9, 10 minus one empty.
After placing B(5), H(6), F(7), E(10): seat 9 is empty.

Step 6: Final arrangement
Seat: 1(_) 2(A) 3(G) 4(D) 5(B) 6(H) 7(F) 8(C) 9(_) 10(E)

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: A, G, D, B, H, F, C = 7 persons

Verification:
βœ“ G at seat 3
βœ“ C at seat 8
βœ“ Empty at seat 1 (extreme end)
βœ“ A immediately right of empty seat 1
βœ“ D fourth to left of C (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

Question 19

Eight persons D, C, G, A, B, H, F and E are sitting around a square table. Four persons sit at corners and four at the middle of sides, all facing the center. D sits at a corner. C sits second to the right of D. G sits at the middle of a side and is not adjacent to D. A sits opposite to D. B sits at a corner immediately to the right of G. H sits immediately to the left of C. F is not adjacent to A. How many persons sit between D and A when counted from the left of D?
Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) β†’ M1(2) β†’ C2(3) β†’ M2(4) β†’ C3(5) β†’ M3(6) β†’ C4(7) β†’ M4(8) β†’ back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- D sits at a corner β†’ pos 1
- C sits second to the RIGHT of D: right(center-facing)=CW
2 CW from pos 1 β†’ pos 3 βœ“ (corner)
- A sits OPPOSITE D (pos 1) β†’ pos 5 βœ“
- G at midpoint, NOT adjacent to D(pos 1):
Adjacent to pos 1: pos 8 and pos 2
G β†’ pos 6 (midpoint, not adjacent) βœ“
- B sits at corner immediately to the RIGHT of G(pos 6):
1 CW from pos 6 β†’ pos 7 (corner) βœ“

Step 3: Remaining persons
Remaining: H, F, E
Fill remaining seats: pos2=H, pos8=F, pos4=E

Final Arrangement (clockwise):
pos1:D β†’ pos2:H β†’ pos3:C β†’ pos4:E β†’ pos5:A β†’ pos6:G β†’ pos7:B β†’ pos8:F

Step 4: Count from LEFT of D to A
Left = anti-clockwise direction from D(pos 1):
pos1(D) β†’ pos8(F) β†’ pos7(B) β†’ pos6(G) β†’ pos5(A)
Persons between (excluding D and A): pos8(F), pos7(B), pos6(G)
Count = 3 person(s)

Answer: Three person(s) sit between D and A.

Question 20

Six persons Bhanu, Farhan, Aman, Deepak, Esha and Charu are sitting around a hexagonal table, one at each corner, all facing the center. Bhanu sits opposite to Farhan. Aman sits second to the right of Bhanu. Esha sits second to the right of Charu. Deepak is not adjacent to Bhanu. What is the position of Deepak with respect to Aman?
Solution Approach:

Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Bhanu at H1 (pos 1).
- Bhanu opposite Farhan: opp(pos1) = pos4 β†’ Farhan at H4

Step 3: Apply relative positioning
- Aman second to the right of Bhanu(pos1):
CW 2: pos1β†’pos2β†’pos3
β†’ Aman at H3

- Esha second to the right of Charu:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Bhanu=1, Farhan=4, Aman=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Charu: pos5 is 2 clockwise [solver-verified].
β†’ Charu at pos6, Esha at pos2

Step 4: Apply constraint
- Deepak not adjacent to Bhanu(pos1):
Adjacent to pos1: pos6 and pos2
β†’ Deepak at pos5 (not adjacent) βœ“

Final Arrangement (clockwise):
H1:Bhanu β†’ H2:Esha β†’ H3:Aman β†’ H4:Farhan β†’ H5:Deepak β†’ H6:Charu

Step 5: Find Deepak's position relative to Aman
Aman at pos3, Deepak at pos5.
pos5 is 2 clockwise from pos3.

Verification:
βœ“ Bhanu opposite Farhan
βœ“ Aman second to right of Bhanu
βœ“ Esha second to right of Charu
βœ“ Deepak not adjacent to Bhanu

Answer: Deepak sits to the second to the right of Aman.
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