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Seating Arrangement

28 questions

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Question 1Question →

Six family members—Arthur, Beatrice, Clara, David, Elena, and Felix—are sitting around a circular table facing the center for dinner.

The seating arrangement is based on the following conditions:
1. Arthur is sitting directly opposite David.
2. Beatrice is sitting immediately to the right of Arthur.
3. Clara is sitting exactly between David and Beatrice.
4. Elena is sitting immediately to the left of Arthur.

Based on this information, who is sitting immediately to the right of David?

Show answer & explanation

Answer: Felix

Answer

Felix
By successfully mapping the circular arrangement, all family members are placed. Since Felix is the only one left without an explicitly stated position, he takes the final empty seat. This seat is located immediately to the right of David, making Felix the correct answer.

Step-by-Step Solution

1
Visualize or draw a circle with 6 equally spaced seats and place Arthur at one of the seats.
Arthur is assigned a position. For reference, let's place Arthur at the bottom (6 o'clock).
Setting a fixed starting point makes relative placements much easier.
2
Place David based on the first condition.
David is placed at the top (12 o'clock), directly opposite Arthur.
The condition states Arthur and David sit directly opposite each other.
3
Place Beatrice and Elena relative to Arthur.
Beatrice goes to the immediate right of Arthur (4 o'clock, counter-clockwise). Elena goes to the immediate left of Arthur (8 o'clock, clockwise).
Because everyone is facing the center, 'right' is counter-clockwise and 'left' is clockwise from the perspective of the person sitting.
4
Place Clara based on her position relative to David and Beatrice.
Clara is placed at 2 o'clock, which is the only seat exactly between David (12 o'clock) and Beatrice (4 o'clock).
The condition explicitly places Clara between these two specific family members.
5
Determine Felix's position and answer the final question.
Felix must occupy the last remaining seat at 10 o'clock. Since David is at 12 o'clock facing the center, his immediate right (counter-clockwise) is 10 o'clock, where Felix is sitting.
All other family members are placed. The question asks for the person to the immediate right of David.

Key Concept

Circular Seating Arrangements
Question 2Question →

Six historic ships��Bounty, Cutty Sark, Discovery, Endeavour, Mayflower, and Victoria—are anchored in a single straight row facing North (towards the harbor). Their left-to-right positions are determined by the following conditions:

1. The Discovery is anchored at the extreme left end of the row.
2. The Victoria is anchored exactly midway between the Mayflower and the Endeavour.
3. The Bounty anchors immediately to the right of the Mayflower.
4. The Cutty Sark anchors immediately to the left of the Endeavour.
5. The Cutty Sark and the Victoria are anchored next to each other.

Arrange the ships in the correct order from the extreme left (1st position) to the extreme right (6th position).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from left to right is: Discovery, Mayflower, Bounty, Victoria, Cutty Sark, Endeavour.
The correct sequence is established by recognizing how the adjacency rules merge into larger blocks. By deducing that the Cutty Sark and Endeavour form a 'C-E' pair, and Victoria must sit next to Cutty Sark to form 'V-C-E', we establish the exact distance between Victoria and Endeavour (2 positions). Because Victoria must be midway between Mayflower and Endeavour, the Mayflower must also be exactly 2 positions away on the opposite side. This forces the 'Mayflower-Bounty' pair to sit immediately left of Victoria, yielding a unified 5-ship block 'M-B-V-C-E' that perfectly slots in next to the Discovery.

Step-by-Step Solution

1
Establish the given anchor.
Position 1 is Discovery (D). The sequence is currently D, _, _, _, _, _.
Condition 1 explicitly states Discovery is at the extreme left end.
2
Combine adjacency conditions to form fixed spatial blocks.
We identify a two-ship block (M - B) and a three-ship block (V - C - E).
Condition 4 requires Cutty Sark (C) to be immediately left of Endeavour (E), forming 'C - E'. Condition 5 requires Victoria (V) to be next to C. Since placing V to the right of C would break the 'C - E' block, V must be immediately to the left of C, forming 'V - C - E'. Condition 3 requires Bounty (B) to be immediately right of Mayflower (M), forming 'M - B'.
3
Apply the midway condition to combine the blocks into a single sequence.
The combined sequence becomes M - B - V - C - E.
Condition 2 states V is exactly midway between M and E. In our 'V - C - E' block, E is exactly two positions to the right of V. Therefore, M must be exactly two positions to the left of V. Placing the 'M - B' block immediately before V perfectly satisfies this midway requirement.
4
Finalize the arrangement by placing the unified block.
The final arrangement is D, M, B, V, C, E.
We have a solid 5-ship sequence (M - B - V - C - E). With Discovery anchored at position 1, the only way to fit the remaining 5 ships is consecutively in positions 2 through 6.

Key Concept

Linear seating arrangement combining relative positional blocks and distance/midpoint constraints.
Estimated Time:2m 30s
Question 3Question →

Eight friends—S, T, U, V, W, X, Y, and Z—are sitting in a straight line facing North.

- V sits fourth to the left of W.
- W sits at one of the extreme ends of the line.
- Only two people sit between V and X.
- Y sits third to the right of S.
- S is not an immediate neighbor of V.
- Z sits to the immediate left of T.

Which of the following statements are correct?

Select all that apply

Show answer & explanation

Answer: U sits exactly between S and V.; Y sits second to the left of T.

Answer

The statements 'U sits exactly between S and V' and 'Y sits second to the left of T' are correct.
Based on the systematic deduction of the constraints, the exact left-to-right order of the eight friends is X, S, U, V, Y, Z, T, W. In this confirmed arrangement, U (position 3) is situated directly between S (position 2) and V (position 4). Additionally, T is at position 7, meaning the second position to its left is position 5, which is exactly where Y sits.

Step-by-Step Solution

1
Determine the positions of W and V.
W is at position 8 (extreme right) and V is at position 4.
W is at an extreme end, and V is 4th to the left of W. If W were at the left end (position 1), V couldn't physically be to its left. Thus, W must be at the extreme right (8). Counting 4 spots left places V at 4.
2
Locate X based on V's position.
X must be at position 1.
Two people sit between V (4) and X. This means X can either be at 1 or 7. We test both possibilities in the next steps.
3
Evaluate the scenario where X is at position 7.
This scenario leads to a logical contradiction and is eliminated.
If X=7, S (who cannot be adjacent to V at 3 or 5) must be at 1 or 2. If S=1, Y becomes 4, which is already occupied by V. If S=2, Y becomes 5. This leaves spots 1, 3, and 6 empty. However, Z and T require adjacent spots, which are unavailable here. Thus, X cannot be 7.
4
Finalize positions with X at position 1.
The final arrangement from left to right is: X, S, U, V, Y, Z, T, W.
With X=1, testing valid spots for S yields S=2 (since S cannot be 3 or 5) and Y=5. The remaining empty spots are 3, 6, and 7. Since Z sits to the immediate left of T, they must take the adjacent spots 6 and 7 (Z=6, T=7). U must take the last remaining spot, which is 3.

Key Concept

Linear Seating Arrangement with North-Facing Orientation
Question 4Question →

Six professionals — P, Q, R, S, T, and U — sit around a circular table, with some facing the center and others facing outward. Q faces the center. P sits second to the right of Q. U is not an immediate neighbor of Q, and T sits to the immediate right of U. R sits to the immediate left of P. S sits second to the right of R. P and R face the same direction, while U and P face opposite directions. The immediate neighbors of T face the same direction. Finally, S and T face the same direction as Q.

Based on the given information, who sits to the immediate right of P?

Show answer & explanation

Answer: S

Answer

S
Based on the seating arrangement logic, P is seated at position 5 and is facing outward. For an individual facing outward from the center, their right side follows the clockwise direction. The person seated immediately clockwise to P is S (at position 6). Therefore, S sits to the immediate right of P.

Step-by-Step Solution

1
Place Q and determine P's position.
Q is at position 1 facing the center. P is at position 5.
Since Q faces the center, the right side is counter-clockwise. P sits second to the right of Q (positions: 1 -> 6 -> 5).
2
Determine the positions of U and T.
U is at position 3 facing the center, and T is at position 2.
U cannot be adjacent to Q, leaving positions 3 and 4 available for U. If U is placed at 4, placing T to its immediate right causes a conflict with either P or R's required positions regardless of facing direction. Thus, U must be at position 3. T sits to the immediate right of U.
3
Determine the facing direction of P and place R.
P faces outward, placing R at position 4.
R is to the immediate left of P. If P faced the center, R would be at 6. S (second right of R) would then be at 4, forcing R to face inward. But U and P must face opposite directions, meaning if P is inward, U is outward, which breaks T's placement. Therefore, P must face outward, placing R at position 4.
4
Complete the arrangement with S and verify all conditions.
S is at position 6. R and P face outward. S, T, U, and Q face the center.
S is second to the right of R. Since R faces outward (same as P), right is clockwise (4 -> 5 -> 6). T and S face the same direction as Q (inward). All conditions are satisfied.
5
Identify the person to the immediate right of P.
S sits to the immediate right of P.
P is at position 5 facing outward. For outward-facing positions, right is clockwise. The position immediately clockwise to 5 is 6, which is occupied by S.

Key Concept

Analytical reasoning using circular seating constraints with mixed facing directions (inward and outward).
Question 5Question →

Eight delegates—J, K, L, M, N, O, P, and Q—are seated in two parallel rows containing four people each, such that there is an equal distance between adjacent persons.

In Row-1, J, K, L, and M are seated and all of them are facing South.
In Row-2, N, O, P, and Q are seated and all of them are facing North.
Each member seated in a row faces another member of the other row.

• N sits second to the right of O.
• The person facing N sits to the immediate right of M.
• The person facing L sits to the immediate left of N.
• J is an immediate neighbor of L but does not face O.
• Q does not sit at an extreme end of the row.

Based on the given seating arrangement, which of the following statements are correct? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: L faces Q, who sits second to the left of P.; J sits to the immediate left of L.

Answer

The statements 'L faces Q, who sits second to the left of P' and 'J sits to the immediate left of L' are correct.
The correct statements accurately reflect the finalized arrangement. L is at Position 2 (Row-1) facing Q at Position 2 (Row-2). Since P is at Position 4 (Row-2, facing North), Q is exactly second to the left of P. Furthermore, J (Position 3) is to the immediate left of L (Position 2) because they face South, meaning their leftward direction is eastward.

Step-by-Step Solution

1
Determine the valid positions for O and N in Row-2.
O must be at Position 1 and N at Position 3.
N sits second to the right of O (North-facing). If O were at Position 2, N would be at Position 4. In that case, the person facing N (Position 4 in Row-1) would sit to the immediate right of M. Since Row-1 faces South, right means a lower position number on the grid, requiring M to be at Position 5, which is impossible. Thus, O is at Position 1 and N is at Position 3.
2
Determine the position of M in Row-1.
M must sit at Position 4.
N is at Position 3. The person facing N is at Position 3 in Row-1. This person sits to the immediate right of M. Because Row-1 faces South, M must be at Position 4 (to the east of Position 3).
3
Locate the positions of L and Q.
L sits at Position 2 in Row-1, and Q sits at Position 2 in Row-2.
The person facing L sits to the immediate left of N. N is at Position 3 (North-facing), so N's immediate left is Position 2. Thus, the person facing L is at Position 2 in Row-2. This means L is at Position 2 in Row-1. Since Q cannot sit at an extreme end and Position 2 is the only inner seat available in Row-2, Q must sit at Position 2, facing L.
4
Determine the positions of J and K in Row-1.
J sits at Position 3 and K sits at Position 1.
J is an immediate neighbor of L (who is at Position 2), so J is at 1 or 3. If J were at 1, J would face O, contradicting the rule that J does not face O. So J is at 3, leaving Position 1 for K.
5
Determine the final position for P in Row-2.
P sits at Position 4.
The only remaining seat in Row-2 is Position 4, so P must be seated there.

Key Concept

Double parallel row seating arrangements with opposite facing directions.
Estimated Time:2m 30s
Question 6Question →

Seven chefs—A, B, C, D, E, F, and G—are participating in a culinary competition. They are seated in a single straight row facing North for a tasting session.

- C sits third to the right of the person seated at the extreme left end.
- E sits exactly between A and F.
- F does not sit at either of the extreme ends.
- G sits second to the left of B.
- B is not an immediate neighbor of C.

Based on this arrangement, what is the position of F with respect to G?

Show answer & explanation

Answer: Second to the left

Answer

Second to the left
The correct seating sequence from left to right is A, E, F, C, G, D, B. Since F is in the third position and G is in the fifth position, F sits exactly two places to the left of G.

Step-by-Step Solution

1
Determine the absolute position of C in the row.
Since C sits third to the right of the extreme left end (Position 1), C must be seated at Position 4.
This provides a fixed anchor point to evaluate the remaining relative conditions.
2
Determine the possible positions for G and B.
G sits second to the left of B, requiring the pattern (G _ B). B cannot be next to C (Positions 3 or 5). If B is at Position 6, G would be at Position 4, which is occupied. Therefore, B must be at Position 7, placing G at Position 5.
Eliminating invalid placements based on the negative constraint secures the right side of the arrangement.
3
Locate A, E, and F.
E sits exactly between A and F, requiring three consecutive empty seats. The only available consecutive sequence is Positions 1, 2, and 3. Thus, E must take Position 2.
Large contiguous blocks must fit into the remaining consecutive open spaces.
4
Finalize the exact positions of A, F, and D.
Since F cannot sit at an extreme end, F must take Position 3, leaving A at Position 1. The remaining chef, D, must sit in the only remaining seat at Position 6.
Applying the final negative constraint (F not at an end) resolves the ambiguity between A and F.
5
Evaluate F's position relative to G.
The final arrangement from left to right is A, E, F, C, G, D, B. F is at Position 3 and G is at Position 5. Therefore, F is second to the left of G.
This directly answers the specific question asked in the stem.

Key Concept

Linear arrangement with negative constraints and directional orientation
Question 7Question →

Six astronauts—Aldrin, Collins, Glenn, Jemison, Ride, and Shepard—are seated in a single straight row facing the main presentation screen (North) during a mission briefing.

Based on the following conditions, arrange the astronauts in their correct seating order from the leftmost position to the rightmost position:

- Jemison sits third to the right of Collins.
- Ride sits at one of the extreme ends of the row.
- Aldrin sits immediately next to Ride, but is not adjacent to Jemison.
- Shepard sits to the immediate left of Glenn.

Arrange the astronauts in order from Position 1 (far left) to Position 6 (far right).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct left-to-right order is: Ride, Aldrin, Collins, Shepard, Glenn, Jemison.
The correct sequence is derived by testing the possible ends for Ride. If Ride is at the right end (Position 6), Aldrin is at Position 5, which means Jemison cannot be at Position 4 or 6. This makes it impossible for Jemison to be third to the right of Collins. Therefore, Ride must be at the left end (Position 1), placing Aldrin at Position 2. Collins at Position 3 ensures Jemison is at Position 6. Shepard and Glenn then naturally fill Positions 4 and 5 to remain adjacent.

Step-by-Step Solution

1
Determine Ride's possible positions.
Ride is at either Position 1 (far left) or Position 6 (far right).
The conditions state that Ride sits at one of the extreme ends of the row.
2
Test placing Ride at Position 6 (far right).
This configuration is impossible and must be eliminated.
If Ride is at 6, Aldrin must be at 5. Since Jemison cannot sit next to Aldrin, Jemison cannot be at 4 or 6. This leaves no possible way for Jemison to be exactly third to the right of Collins (which would require Jemison to be at 4, 5, or 6).
3
Place Ride at Position 1 and Aldrin at Position 2.
Position 1 = Ride, Position 2 = Aldrin.
Since the right extreme is invalid, Ride must be at the left extreme. Aldrin sits immediately next to Ride.
4
Determine positions for Collins and Jemison.
Position 3 = Collins, Position 6 = Jemison.
Jemison is third to the right of Collins (pattern: Collins - empty - empty - Jemison). The only spaces that can accommodate this spread, without overlapping Aldrin at Position 2, are Positions 3 and 6.
5
Place the remaining pair, Shepard and Glenn.
Position 4 = Shepard, Position 5 = Glenn.
Shepard sits immediately to the left of Glenn. Positions 4 and 5 are the only two consecutive empty seats left in the row.

Key Concept

Logical deduction in linear arrangements by testing extreme edge cases to eliminate contradictions.
Question 8Question →

Seven investors—M, N, O, P, Q, R, and S—are sitting around a circular table for a portfolio review. All of them are facing away from the center of the table.

1. S sits second to the right of R.
2. M sits third to the left of R.
3. O sits to the immediate left of M.
4. P sits exactly between R and S.
5. Q is an immediate neighbor of N, but Q is not an immediate neighbor of M.

What is the position of Q with respect to R?

Show answer & explanation

Answer: To the immediate left

Answer

To the immediate left
Based on the clues, the final clockwise arrangement starting from R is: R, P, S, O, M, N, Q. When checking Q's position relative to R, Q is situated exactly one position counter-clockwise from R. Because all investors are facing away from the center, counter-clockwise corresponds to the left direction. Therefore, Q sits to the immediate left of R.

Step-by-Step Solution

1
Establish the directional rules based on the facing direction.
Since all investors face away from the center, 'Right' means moving clockwise and 'Left' means moving counter-clockwise around the table.
This is the fundamental rule of circular seating arrangements when individuals face outward.
2
Place R as the starting reference point and position S, M, and O.
Assign R to position 1. S is second to the right (clockwise), placing S at position 3. M is third to the left (counter-clockwise), placing M at position 5. O is to the immediate left (counter-clockwise) of M, placing O at position 4.
Applying direct positional clues 1, 2, and 3 establishes the primary framework.
3
Determine the position of P.
P sits exactly between R (position 1) and S (position 3). Therefore, P must sit at position 2.
Fulfilling clue 4 fills the gap between R and S.
4
Position Q and N using the remaining seats and constraints.
The remaining empty seats are 6 and 7. Q and N must occupy them since they are immediate neighbors. Clue 5 states Q is not a neighbor of M (who is at position 5). Therefore, Q cannot be at position 6 and must be at position 7, leaving N at position 6.
Applying the final clues and the process of elimination completes the seating arrangement.
5
Determine Q's position with respect to R.
R is at position 1 and Q is at position 7. Position 7 is one step counter-clockwise from position 1. Since counter-clockwise is left, Q is to the immediate left of R.
Answering the specific question asked in the stem based on the completed arrangement.

Key Concept

Circular Seating Arrangement (Outward Facing)
Question 9Question →

Seven colleagues—T, U, V, W, X, Y, and Z—are seated in a straight line. Some of them are facing North while others are facing South.

- T sits exactly in the middle of the line and faces North.
- W sits second to the left of T.
- U sits third to the right of W.
- Only one person sits between U and X.
- Y sits to the immediate right of X.
- V sits third to the right of Y.
- The immediate neighbors of T face opposite directions (i.e., if one faces North, the other faces South, and vice versa).
- Persons sitting at the extreme ends of the line face opposite directions.
- Z and U face the same direction, which is opposite to the direction faced by V.

Based on the given seating arrangement, which of the following statements are correct?

Select all that apply

Show answer & explanation

Answer: Z sits to the immediate left of W.; Three people sit between V and X.

Answer

The correct statements are that Z sits to the immediate left of W, and three people sit between V and X.
Based on the step-by-step seating arrangement, the final left-to-right order is Z(North), W(North), V(South), T(North), U(North), Y(South), and X(South). Therefore, Z is to the immediate left of W, and there are three people (T, U, Y) sitting between V and X.

Step-by-Step Solution

1
Place T in the middle of the 7 positions and determine W's position.
T is at position 4 facing North. W is at position 2.
The middle of 7 spots is the 4th spot. W is second to the left of T, who is facing North.
2
Determine the position and facing direction of W, then place U.
W faces North, and U is placed at position 5.
U sits third to the right of W. If W faced South, the 3rd right would be off the line to the left (position -1). Thus, W faces North, placing U at position 5.
3
Locate X and Y based on U's position.
X is at position 7 facing South, and Y is at position 6.
Only one person sits between U (position 5) and X, so X must be at position 3 or 7. However, if X is at 3, Y cannot be to the immediate right (positions 2 and 4 are occupied). Thus, X is at 7. For Y to be at position 6, X must face South.
4
Place V and deduce Y's facing direction.
Y faces South, and V is placed at position 3.
V sits third to the right of Y. If Y faced North, the 3rd right would be position 9 (invalid). Therefore, Y faces South, placing V at position 3.
5
Place Z and determine all remaining facing directions.
Z is at position 1 facing North. U faces North, and V faces South.
Z takes the only empty spot. Extreme ends face opposite directions; X faces South, so Z faces North. Z and U face the same direction (North), opposite to V (South). This perfectly matches the condition that T's neighbors (V and U) face opposite directions.

Key Concept

Analytical seating arrangements with mixed facing directions (North and South).
Question 10Question →

Eight architects—Harper, Ingram, Jenkins, Knox, Larson, Miller, Novak, and Ortiz—are sitting in two parallel rows containing four people each, such that there is an equal distance between adjacent persons.

In Row 1, Harper, Ingram, Jenkins, and Knox are seated, and all of them are facing South.
In Row 2, Larson, Miller, Novak, and Ortiz are seated, and all of them are facing North.
Therefore, each person in Row 1 faces a person in Row 2.

The following information is given about their seating arrangement:
- Jenkins does not sit at an extreme end of the row.
- Harper sits second to the left of Jenkins.
- Larson faces Harper and sits to the immediate right of Ortiz.
- Novak sits at one of the extreme ends of the row but does not face Jenkins.
- Only one person sits between Miller and Larson.
- Ingram faces Novak.

Based on the given arrangement, who sits to the immediate left of Knox?

Show answer & explanation

Answer: Harper

Answer

Harper
Based on the seating clues, Row 1 (South-facing) from viewer's left to right is: Ingram, Jenkins, Knox, and Harper. Knox is seated in the third position. Because he is facing South, his 'left' points toward the viewer's right. Therefore, the person sitting to his immediate left is Harper, who is in the fourth position.

Step-by-Step Solution

1
Establish the directional framework for both rows.
Row 1 faces South (their left is our right). Row 2 faces North (their left is our left). Let's number positions 1 to 4 from our left to right.
Correctly orienting left and right based on facing direction is the most critical step to avoid inversion errors.
2
Place Jenkins and Harper in Row 1 using the first two clues.
Jenkins is at position 2 and Harper is at position 4.
Jenkins cannot be at extreme ends (1 or 4). Harper is second to the left of Jenkins. Since Row 1 faces South, 'left' means moving to our right. The only way Jenkins can have someone two spots to their left without being on an edge is if Jenkins is at position 2 and Harper is at position 4.
3
Place Larson and Ortiz in Row 2.
Larson is at position 4 and Ortiz is at position 3.
Larson faces Harper (position 4). Larson sits to the immediate right of Ortiz. Since Row 2 faces North, 'right' is our right, meaning Ortiz must be just left of Larson at position 3.
4
Place Miller and Novak in Row 2.
Miller is at position 2 and Novak is at position 1.
There is one person between Miller and Larson (position 4), forcing Miller to position 2. Novak is at an extreme end, leaving only position 1 open. Novak at position 1 does not face Jenkins (at position 2), satisfying the condition.
5
Complete Row 1 by placing Ingram and Knox.
Ingram is at position 1 and Knox is at position 3.
Ingram faces Novak (position 1). This leaves only position 3 for Knox.
6
Determine who sits to the immediate left of Knox.
Harper sits to the immediate left of Knox.
Knox is at position 3 facing South. His immediate left is our right, which is position 4. Harper occupies position 4.

Key Concept

Linear Seating Arrangement with Multiple Facing Directions
Question 11Question →

Five executives—Ford, Greta, Harry, Ian, and Julia—are seated in a single straight row facing South during a board meeting.

Based on the following conditions, arrange the executives in the exact order they are seated from West to East (i.e., from the viewer's left to right):

1. Ford sits at the extreme left end of the row.
2. Julia sits immediately to the right of Ford.
3. Greta sits second to the right of Ian.
4. Harry sits adjacent to Ian, but does not sit next to Julia.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct seating order from West to East (viewer's left to right) is Greta, Harry, Ian, Julia, and Ford.
By accounting for the South-facing orientation, we reverse the standard left and right. Ford at the 'extreme left' places him on the viewer's far right (East). Following the relative positioning places Julia beside him, Ian in the middle, Harry at position 2, and Greta at position 1 (West).

Step-by-Step Solution

1
Determine the layout based on the facing direction.
Create five seats from West (viewer's left) to East (viewer's right). Since they face South, an executive's 'left' corresponds to East and their 'right' corresponds to West.
Crucial for correctly interpreting spatial clues without reversing the arrangement.
2
Place Ford and Julia using clues 1 and 2.
Ford is placed at position 5 (East/extreme left). Julia is placed at position 4 (immediate right of Ford).
Ford is at the extreme left (which is East when facing South). Julia is to his immediate right (which is West).
3
Place Ian and Greta using clue 3.
Ian is placed at position 3 and Greta is placed at position 1.
Greta is second to the right of Ian. The only remaining spaces with a gap of one seat are positions 1 and 3 (right = West).
4
Place Harry using clue 4.
Harry is placed at position 2.
Harry must be adjacent to Ian (position 3), which means he must be at position 2 or 4. Position 4 is occupied by Julia, so Harry takes position 2. This perfectly satisfies the condition that he is not next to Julia.

Key Concept

Linear Seating Arrangement with South-Facing Orientation
Question 12Question →

Six city planners—David, Elena, Felix, Grace, Hassan, and Iris—are sitting around a circular table for a development meeting. Some planners are facing the center of the table while others are facing outward.

Based on the following conditions, determine their exact seating arrangement:
1. David and Grace sit opposite each other, and both are facing the center.
2. Elena sits to the immediate left of David.
3. Iris sits second to the left of Elena.
4. Felix sits to the immediate right of Grace.
5. Elena, Hassan, and Iris all face the same direction.
6. Felix faces the opposite direction to Hassan.

Based on the seating arrangement, who sits to the immediate left of Hassan?

Show answer & explanation

Answer: Grace

Answer

Grace sits to the immediate left of Hassan.
Based on the clues, Hassan sits between Grace and Iris, facing outward. When facing outward, a person's left side corresponds to the counter-clockwise direction along the circle. The person seated immediately counter-clockwise to Hassan is Grace.

Step-by-Step Solution

1
Place David and Grace on a 6-position circular diagram.
David is at position 1 and Grace is at position 4. Both face the center.
Clue 1 states they sit opposite each other and both face the center.
2
Determine Elena's position and facing direction.
Elena is at position 2 and faces outward.
Clue 2 says Elena is to the immediate left of David. Since David faces the center, his left is clockwise, placing Elena at position 2. Clue 3 states Iris is second to Elena's left. If Elena faced the center, her second left would be position 4 (occupied by Grace). Thus, Elena must face outward.
3
Determine Iris's position.
Iris sits at position 6.
Since Elena is at position 2 and faces outward, 'left' means moving counter-clockwise. Two positions counter-clockwise from position 2 is position 6.
4
Place Felix and the remaining person, Hassan.
Felix is at position 3, and Hassan is at position 5.
Clue 4 states Felix is to the immediate right of Grace. Grace faces the center, so her right is counter-clockwise, which is position 3. Hassan must take the only remaining seat at position 5.
5
Determine the facing directions for Hassan, Iris, and Felix.
Hassan and Iris face outward. Felix faces the center.
Clue 5 states Elena, Hassan, and Iris face the same direction. Since Elena faces outward, Hassan and Iris also face outward. Clue 6 states Felix faces opposite to Hassan, so Felix faces the center.
6
Find the person to the immediate left of Hassan.
Grace
Hassan is at position 5 facing outward. For an outward-facing person, 'left' is counter-clockwise. The seat counter-clockwise from position 5 is position 4, which is occupied by Grace.

Key Concept

Mixed-facing circular seating arrangements and relative directional positioning based on orientation.
Question 13Question →

Eight colleagues—K, L, M, N, O, P, Q, and R—are sitting around a square table. Four of them sit in the middle of the sides and face the center of the table, while the other four sit at the four corners and face outside (away from the center). They are seated according to the following conditions:

- M sits in the middle of one of the sides.
- K sits third to the left of M.
- Only two people sit between K and R.
- O sits to the immediate right of R.
- P sits second to the left of K.
- N is an immediate neighbor of O.
- Q sits to the immediate right of P.

Based on the given seating arrangement, which of the following statements are correct? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: L sits to the immediate right of M.; Exactly three people sit between K and L when counted from the right of K.

Answer

The correct statements are that L sits to the immediate right of M, and exactly three people sit between K and L when counted from the right of K.
Based on the seating conditions, M is at a middle position (facing center). K is 3rd to the left (clockwise), placing K at a corner facing outside. R is separated from K by two people, meaning R is at the opposite middle position (facing center). O is to the immediate right of R (counter-clockwise), placing O at a corner facing outside. P is 2nd to the left of K (counter-clockwise), so P is at a corner. N is O's neighbor, leaving only one adjacent spot. Q is immediate right of P (clockwise). L takes the last spot. In this final layout, L is immediately counter-clockwise from M, which is M's right side, making the first statement correct. Counting clockwise from K (K's right side), we pass N, O, and R before reaching L, making the statement about three people between K and L correct.

Step-by-Step Solution

1
Determine M and K's positions.
M is at a middle position (facing center). K is 3rd to the left of M. Since M faces the center, left is clockwise, placing K at a corner (facing outside).
M is explicitly given as sitting in the middle. The direction rules (center = left is clockwise) determine K's placement.
2
Determine R and O's positions.
R must be at the opposite middle position (facing center). O is to the immediate right of R, placing O at the adjacent corner counter-clockwise (facing outside).
Only two people sit between K and R, so R is opposite M. R faces the center, so its right is counter-clockwise.
3
Place P, N, Q, and L.
P is 2nd to the left of K (counter-clockwise), N is the only available neighbor of O, Q is to the immediate right of P (clockwise), and L takes the final remaining position.
Following the remaining clues step-by-step while strictly adhering to the left/right rules for inward vs. outward facing positions ensures a unique arrangement.
4
Evaluate the given statements based on the final arrangement.
The statements about L's position relative to M, and the number of people between K and L (counting from K's right) are correct.
By applying the left/right rules to the completed seating layout, we can confirm the validity of each statement.

Key Concept

Polygonal Seating Arrangement with Mixed Facing Directions
Estimated Time:2m 0s
Question 14Question →

Five delegates—Alice, Ben, Clara, David, and Emma—are sitting in a single straight row facing North during a conference.

Read the following conditions carefully:
1. David is sitting at the extreme left end of the row.
2. Ben is sitting second to the right of Alice.
3. Clara is an immediate neighbor of Ben, but does not sit next to Alice.

Arrange the delegates in their correct seating order from the extreme left end to the extreme right end of the row.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from left to right is: David, Alice, Emma, Ben, Clara.
The arrangement must logically begin with David at position 1. Alice must sit at position 2 and Ben at position 4; otherwise, Clara would be forced to sit next to Alice (if Alice were at 3 and Ben at 5). Consequently, Clara takes position 5, leaving position 3 for Emma.

Step-by-Step Solution

1
Place David according to the first condition.
David is at position 1. The row configuration from left to right is: David, _, _, _, _.
The condition explicitly states David is at the extreme left end.
2
Determine the possible positions for Alice and Ben.
Since Ben is second to the right of Alice, the possible position pairs for (Alice, Ben) are (2, 4) or (3, 5).
This maintains exactly one empty seat between Alice and Ben to her right.
3
Evaluate the (3, 5) position pair using Clara's constraint.
If Alice is at 3 and Ben is at 5, Clara must be at 4 to be an immediate neighbor of Ben. However, this places Clara next to Alice, which violates the third condition.
Testing hypotheses against negative constraints is necessary to eliminate invalid scenarios.
4
Place Alice, Ben, and Clara in the only valid remaining configuration.
Alice is securely at position 2, and Ben is at position 4. Clara must sit at position 5 to be next to Ben but not next to Alice.
This is the only configuration that satisfies both the 'second to the right' rule and the negative neighbor constraint.
5
Place Emma in the final remaining seat.
Emma sits at position 3. The final order is David, Alice, Emma, Ben, Clara.
There is only one person left (Emma) and one seat available (position 3).

Key Concept

Linear Seating Arrangement with negative constraints
Question 15Question →

Seven diplomats—Alan, Boris, Chloe, David, Elena, Felix, and Grace—are sitting around a circular table facing the center.

Read the following conditions carefully:
1. Alan sits third to the right of Boris.
2. Chloe sits second to the left of Alan.
3. David sits immediately between Elena and Felix.
4. Elena is not an immediate neighbor of Boris.

Based on the above seating arrangement, who sits second to the right of Grace?

Show answer & explanation

Answer: Elena

Answer

Elena sits second to the right of Grace.
Following the conditions step-by-step: If we place Boris at position 1, Alan goes to position 4 (third to the right, anti-clockwise). Chloe goes to position 2 (second to the left of Alan, clockwise). The three consecutive seats for Elena, David, and Felix must be 5, 6, and 7, meaning David is at 6. Grace takes the only empty seat at 3. Because Elena cannot be next to Boris (position 1), she must take position 5, leaving Felix at position 7. The complete anti-clockwise order is Boris, Chloe, Grace, Alan, Elena, David, Felix. Grace is at position 3; the second person to her right is at position 5, which is occupied by Elena.

Step-by-Step Solution

1
Place Boris and determine Alan's position using the first condition.
Assume Boris is at position 1. Since they face the center, 'right' is anti-clockwise. Alan is third to the right, placing him at position 4.
Fixing a reference point is the standard method for solving circular arrangements.
2
Place Chloe using the second condition.
Chloe sits second to the left (clockwise) of Alan (position 4). Thus, Chloe is placed at position 2.
Chloe's position is strictly relative to Alan's fixed position.
3
Identify the seating block for David, Elena, and Felix.
David sits immediately between Elena and Felix, requiring three consecutive empty seats. The currently occupied seats are 1, 2, and 4. The only consecutive empty seats are 5, 6, and 7. Therefore, David must sit exactly in the middle of them, at position 6.
This is the only way to satisfy the requirement of three people sitting together without splitting the group.
4
Place Grace in the arrangement.
With positions 1, 2, 4, 5, 6, and 7 accounted for, position 3 is the only remaining seat. Grace must sit at position 3.
By the process of elimination, the last remaining person takes the last available seat.
5
Determine the exact positions of Elena and Felix using the final condition.
Elena and Felix occupy positions 5 and 7 in some order. Boris is at position 1, making positions 2 and 7 his immediate neighbors. Since Elena cannot be an immediate neighbor of Boris, she cannot sit at position 7. Therefore, Elena is at position 5, and Felix is at position 7.
This fully resolves all ambiguities in the arrangement while satisfying the negative constraint.
6
Answer the specific question asked in the stem.
Grace is at position 3. Facing the center, the second seat to her right (anti-clockwise) is position 5. Elena occupies position 5.
Applying the final relative directional check on the completed diagram.

Key Concept

Solving complex circular seating arrangements by logically deducing relative positions and applying negative constraints.
Question 16Question →

Eight students—P, Q, R, S, T, U, V, and W—are seated in two parallel rows containing four people each, such that there is an equal distance between adjacent persons.

In Row 1, P, Q, R, and S are seated and all of them are facing South.
In Row 2, T, U, V, and W are seated and all of them are facing North.
In the given seating arrangement, each member seated in a row faces another member of the other row.

- Q sits second to the left of S.
- The person facing Q sits to the immediate right of W.
- P sits at one of the extreme ends of the row.
- V faces the person who sits to the immediate right of R.
- T sits at an extreme end of the row, and does not face P.

Based on the given arrangement, which of the following statements are correct? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: U sits at an extreme end of the row and faces P.; R faces the person who sits to the immediate left of T.

Answer

The correct statements are that U sits at an extreme end facing P, and R faces the person who sits to the immediate left of T.
Based on the final arrangement, U is at the leftmost extreme end of Row 2 and faces P at the leftmost extreme end of Row 1, making the statement about U correct. T is at the rightmost extreme end of Row 2 facing North, meaning W is to T's immediate left; R sits directly opposite W, making the statement about R correct.

Step-by-Step Solution

1
Establish the left and right directions for both rows based on their facing directions.
Row 1 (South): Left is rightward, Right is leftward (from the observer's view). Row 2 (North): Left is leftward, Right is rightward.
Correctly orienting directions is critical before placing individuals in a parallel arrangement.
2
Place S and Q using the clue: 'Q sits second to the left of S'.
Since S faces South, 'left' means moving to the observer's right. Possibility 1: S is at position 1 (far left), Q is at position 3. Possibility 2: S is at position 2, Q is at position 4.
This establishes the relative spacing between two individuals in Row 1.
3
Incorporate the clues about W and P to test the possibilities.
Using 'P sits at an extreme end': In Possibility 1, P must be at 4. In Possibility 2, P must be at 1. Using 'The person facing Q sits to the immediate right of W': In Possibility 1, Q(3) faces pos 3. W must be at 2. In Possibility 2, Q(4) faces pos 4. W must be at 3.
Combining extreme end constraints with facing constraints helps fill the grid.
4
Apply the clue regarding V and R: 'V faces the person who sits to the immediate right of R'.
In Possibility 1, the remaining Row 1 person R is at 2. R's right (facing South) is pos 1 (S). V faces S, so V is at 1. In Possibility 2, R is at 3. R's right is pos 2 (S). V faces S, so V is at 2.
This locks in the position of V in Row 2 based on the remaining individuals in Row 1.
5
Resolve the final positions using the clue: 'T sits at an extreme end... and does not face P'.
In Possibility 1, V=1, W=2. T must be at 4 (extreme end). But P is at 4, meaning T faces P, which violates the condition. Thus, Possibility 1 is invalid. In Possibility 2, V=2, W=3. T must be at 1 or 4. If T is at 1, T faces P (at 1), violating the condition. Therefore, T must be at 4. The remaining person U goes to position 1.
This eliminates the invalid scenario and provides the single correct final arrangement.
6
Document the finalized seating grid.
Row 1 (South-facing, left-to-right): P, S, R, Q. Row 2 (North-facing, left-to-right): U, V, W, T.
A complete layout is required to evaluate the given statements in the options.

Key Concept

Applying relative directional reasoning (left/right inversion) in a two-row parallel seating arrangement.
Question 17Question →

Seven researchers—Fiona, George, Harry, Iris, Jack, Kelly, and Liam—are sitting around a circular table for a meeting. Four of them face the center, while the remaining three face outward. They are seated according to the following conditions:

1. Harry faces outward. Jack sits second to the left of Harry.
2. Fiona sits exactly between Harry and George.
3. George sits adjacent to Iris and faces the center.
4. Iris sits second to the right of Jack.
5. Kelly is not an immediate neighbor of Harry and faces the same direction as George.
6. The immediate neighbors of Jack face opposite directions (i.e., one faces the center and the other faces outward).
7. Fiona faces the center.

Based on the given information, who sits third to the left of Kelly?

Show answer & explanation

Answer: Harry

Answer

The correct person sitting third to the left of Kelly is Harry.
Based on the conditions, Kelly must sit in seat 5 facing the center, while Harry sits in seat 1 facing outward. Since Kelly is facing the center, her left direction moves clockwise. Moving three positions clockwise from seat 5 (to 6, then 7, then 1) lands exactly on Harry.

Step-by-Step Solution

1
Set up a 7-seat circular arrangement (numbered 1 to 7 clockwise) and place Harry and Jack.
Harry is at seat 1 facing outward. Jack is at seat 6.
Since Harry faces outward, his 'left' direction is counter-clockwise. Second to the left of seat 1 (counter-clockwise) is seat 7, then seat 6.
2
Place Fiona and George based on relative positions.
Fiona is at seat 2 and George is at seat 3.
Fiona must be exactly between Harry (1) and George. This forces them to occupy consecutive seats (1, 2, 3), placing Fiona at 2 and George at 3. George is given as facing the center. Fiona is given as facing the center.
3
Place Iris and determine Jack's facing direction.
Iris is at seat 4, and Jack faces the center.
George (3) is adjacent to Iris. Since Fiona is already at 2, Iris must be at 4. Iris (4) is second to the right of Jack (6). For seat 4 to be on the right of seat 6 (a counter-clockwise move), Jack must face the center.
4
Place Kelly and Liam, and deduce the remaining directions.
Kelly is at seat 5 facing the center, and Liam is at seat 7 facing outward. Iris faces outward.
Kelly cannot be next to Harry (1), so Kelly cannot take seat 7. Kelly takes seat 5, leaving seat 7 for Liam. Kelly faces the same direction as George (center). Jack's neighbors are Kelly (5) and Liam (7). Since Kelly faces center, Liam must face outward. We now have 4 facing center (Fiona, George, Jack, Kelly), meaning the rest (Harry, Liam, Iris) must face outward.
5
Identify the person sitting third to the left of Kelly.
Harry.
Kelly is at seat 5 facing the center. Left of a center-facing person is clockwise. Tracing three spots clockwise from 5: seat 6 (1st), seat 7 (2nd), and seat 1 (3rd), which is occupied by Harry.

Key Concept

Solving complex circular seating arrangements with mixed facing directions (inward and outward) by tracking relative left-right orientations.
Question 18Question →

Eight executives—K, L, M, N, P, Q, R, and S—are seated in two parallel rows of four members each for a strategic meeting.

Members in Row 1 (P, Q, R, and S) are facing South.
Members in Row 2 (K, L, M, and N) are facing North.
Each executive in Row 1 sits exactly opposite to and faces one executive in Row 2.

The seating arrangement follows these conditions:
1. P sits second to the right of Q.
2. The executive facing Q sits to the immediate right of K.
3. M sits at one of the extreme ends of the row and does not face Q.
4. R sits to the immediate right of P.
5. N is an immediate neighbor of M.

Based on the above arrangement, which of the following statements is true?

Show answer & explanation

Answer: S faces the executive who sits to the immediate left of L.

Answer

The statement 'S faces the executive who sits to the immediate left of L' is true.
Based on the deductions, Row 1 (South) from left to right is R, P, S, Q. Row 2 (North) from left to right is M, N, K, L. The executive sitting to the immediate left of L (who faces North) is K. The executive facing K is S. Therefore, the statement accurately describes the arrangement.

Step-by-Step Solution

1
Determine the layout of Row 1 (South-facing) using conditions 1 and 4.
Row 1 left-to-right (viewer's perspective) is R, P, S, Q.
Since Row 1 faces South, their 'right' is the viewer's left. P sits second to the right of Q means Q is at position 4 and P is at position 2. R sits to the immediate right of P places R at position 1. The remaining seat (position 3) belongs to S.
2
Locate K in Row 2 (North-facing) using condition 2.
K sits at position 3 (viewer's perspective).
Q is at position 4, so the executive facing Q is also at position 4. This person sits to the immediate right of K. Since Row 2 faces North, K must be at position 3 for position 4 to be its immediate right.
3
Place M and N in Row 2 using conditions 3 and 5.
M is at position 1 and N is at position 2.
M is at an extreme end (position 1 or 4) but does not face Q (who is at 4). Therefore, M is at position 1. N is M's immediate neighbor, placing N at position 2.
4
Complete Row 2 and evaluate the options.
Row 2 left-to-right is M, N, K, L. Evaluating the correct option: L is at 4, immediate left is K (at 3), and S (at 3) faces K.
L is the only remaining executive for position 4. Checking the valid spatial relationships against the options proves only one statement is factually accurate.

Key Concept

Linear Seating Arrangement in Dual Parallel Rows
Estimated Time:2m 0s
Question 19Question →

Eight officials (Auditor, Clerk, Governor, Judge, Mayor, Senator, Sheriff, and Treasurer) are seated around a square table. Four of them sit at the corners facing the center of the table, while the other four sit in the middle of each side facing outward away from the center.

- The Sheriff sits at one of the corners.
- The Governor sits third to the right of the Sheriff.
- The Mayor sits second to the right of the Governor.
- The Senator and the Judge are immediate neighbors, but neither is an immediate neighbor of the Governor or the Sheriff.
- The Treasurer sits third to the right of the Judge.
- The Clerk is not an immediate neighbor of the Governor.

Based on the given seating arrangement, which of the following statements are correct?

Select all that apply

Show answer & explanation

Answer: The Clerk and the Governor sit exactly opposite each other.; Exactly three people sit between the Judge and the Mayor.

Answer

The statements indicating that the Clerk and Governor sit opposite each other, and that exactly three people sit between the Judge and the Mayor, are correct.
Based on the systematic deduction of all constraints, the table is arranged as follows (clockwise from top-left): Sheriff, Clerk, Senator, Judge, Auditor, Governor, Treasurer, and Mayor. In this specific configuration, the Clerk and Governor occupy directly opposite middle seats, and the Judge and Mayor occupy opposite middle seats, meaning there are exactly three people between them on either side.

Step-by-Step Solution

1
Establish the directional rules for the inward and outward facing seats.
For the 4 corners facing inward, 'right' moves counter-clockwise and 'left' moves clockwise. For the 4 middle positions facing outward, 'right' moves clockwise and 'left' moves counter-clockwise.
Correctly identifying left and right based on facing direction is mandatory before placing any individuals.
2
Place the Sheriff, Governor, and Mayor to create a foundational layout.
Place the Sheriff at a corner (e.g., top-left, inward). Third to the right (counter-clockwise) places the Governor at the bottom-middle position (outward). Second to the right of the Governor (clockwise) places the Mayor at the left-middle position (outward).
These three linked conditions provide fixed anchor points on the table.
3
Determine the available positions for the Senator and the Judge.
They must sit in adjacent seats but cannot sit next to the Governor or the Sheriff. Eliminating the seats adjacent to the Governor and Sheriff leaves only the top-right corner and the right-middle position as the single valid pair of adjacent seats.
Negative constraints drastically reduce the possible locations for grouped individuals.
4
Differentiate the specific seats for the Senator and the Judge using the Treasurer's condition.
The Treasurer is third to the right of the Judge. If the Judge were at the top-right corner (inward), third to the right would be the left-middle seat, which is already occupied by the Mayor. Thus, the Judge must be at the right-middle seat (outward). Third to the right (clockwise) places the Treasurer at the bottom-left corner. The Senator takes the top-right corner.
Testing the directional constraint ensures no two people are assigned to the same seat.
5
Place the remaining officials, the Clerk and the Auditor.
The remaining empty seats are the top-middle and bottom-right corner. The Clerk cannot be a neighbor of the Governor, so the Clerk takes the top-middle seat. The Auditor fills the final seat at the bottom-right corner.
Applying the final negative constraint finalizes the complete seating arrangement.

Key Concept

Solving complex seating arrangements with mixed facing directions by systematically tracking relative left/right movements.
Question 20Question →

Six journalists—Arthur, Beatrice, Cedric, Daphne, Elias, and Fiona—are seated along one side of a long rectangular press table, all facing the speaker at the front (North). Read the following seating conditions carefully:

1. Arthur is seated third from the left end of the table.
2. Cedric is seated immediately to the right of Arthur.
3. Only one person sits between Cedric and Fiona.
4. Elias sits second to the left of Cedric.
5. Beatrice is not an immediate neighbor of Elias.

Arrange the journalists in their correct seating order from the extreme left end to the extreme right end.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from left to right is Daphne, Elias, Arthur, Cedric, Beatrice, and Fiona.
By following the constraints sequentially, each seat resolves uniquely without any contradiction. Arthur's exact position anchors the arrangement, Cedric and Elias fill in relative to him, and Fiona's distance from Cedric forces her to the end. The negative constraint on Beatrice perfectly resolves the final two seats.

Step-by-Step Solution

1
Identify the total number of positions and place Arthur.
Positions: _ _ Arthur _ _ _
The table has 6 seats. The first condition explicitly places Arthur third from the left.
2
Place Cedric relative to Arthur.
Positions: _ _ Arthur Cedric _ _
The second condition states Cedric sits immediately to the right of Arthur, taking the fourth seat.
3
Place Elias relative to Cedric.
Positions: _ Elias Arthur Cedric _ _
The fourth condition states Elias is second to the left of Cedric. Since Cedric is fourth, Elias must be second.
4
Determine Fiona's position.
Positions: _ Elias Arthur Cedric _ Fiona
The third condition states only one person sits between Cedric and Fiona. This means Fiona is either in seat 2 or 6. Since Elias is already in seat 2, Fiona must take seat 6.
5
Use the negative constraint to place Beatrice.
Positions: _ Elias Arthur Cedric Beatrice Fiona
The fifth condition states Beatrice is not an immediate neighbor of Elias. The empty seats are 1 and 5. Seat 1 is next to Elias, so Beatrice must sit in seat 5.
6
Place the final person, Daphne.
Positions: Daphne Elias Arthur Cedric Beatrice Fiona
Daphne is the only remaining journalist and takes the final empty seat at the extreme left (seat 1).

Key Concept

Linear Seating Arrangement with Positional and Negative Constraints
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