Puzzles & Seating Arrangement — 100 MCQs
Interactive MCQs with hide/show answers and compact explanations.
1. Linear — Simple
Three people A, B, C sit in a row facing north. A sits to the left of B. Who is in the middle?
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Answer: BExplanation: If A is left of B and there are only 3 seats, arrangement (left→right) is A, B, C or C, A, B depending — but facing north left→right is same order. The only way A is left of B and three people fit with B in middle is A, B, C so B is middle.
2. Linear — Facing South
Four people P, Q, R, S sit in a row facing south. P is at the extreme left. Q is immediate right of P. Who sits at extreme right?
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Answer: DExplanation: Facing south flips left/right visually. Given P extreme left and Q immediate right of P, the two remaining seats are R and S; without loss of generality final arrangement is (left→right) P, Q, R, S so S is extreme right.
3. Circular — Basic
Six friends sit around a circle facing the centre. A is opposite D. B sits between A and C. Who is opposite B?
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Answer: CExplanation: If A opposite D, and B between A and C, the seat opposite B must be D if positions are arranged A - B - C - X - D - Y; thus C or D could be opposite depending, but typical arrangement yields D opposite B.
4. Linear — Centres
In a row of 6 facing north the order is E, D, F, C, A, B (left→right). Who are the two middle persons?
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Answer: BExplanation: For 6 people the middle two are positions 3 and 4 which are F and C in given order.
5. Opposite — Table
On one side of a rectangular table sit A, B, C, D; opposite them sit E, F, G, H. A faces E, B faces F, C faces G. Who faces D?
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Answer: DExplanation: If A-E, B-F, C-G are opposite pairs then D must face the remaining person H.
6. Distance — Row
In a row of 12, M is 3rd from left and N is 5th from right. How many people between M and N?
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Answer: BExplanation: M is at position 3 from left (index 3). N is at position 12-5+1 = 8 from left. Number between = 8 - 3 -1 = 4.
7. Facing Direction
Five people face north. If Q is second to left of S, and R sits between P and T, who is at one of the ends?
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Answer: BExplanation: Typical arrangements satisfying the constraints place Q at an end; with limited info the most consistent end-person is Q.
8. Circular — Neighbors
Seven around a circle facing centre. C sits second left of F. G neighbors A and E. A neighbors F. B sits immediate right of E. How many sit between B and F, counting from F's right?
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Answer: DExplanation: Arranging per constraints yields three seats between B and F when counted from F's right.
9. Bench — Ends
Six people A–F face north. A is second right of C (who neighbors D). E is immediate left of A. F neighbors both D and B. B at one end. Who sits at the other end?
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Answer: DExplanation: With B at one end and following constraints, A ends up at the opposite end.
10. Three-row table
Eight people sit around a table (circle). If P is opposite R and S between P and Q, who is opposite Q?
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Answer: DExplanation: With given minimal constraints, exact opposite of Q cannot be determined uniquely.
11. Row — Counting
In a queue of 10 facing north A is 2nd from left and B is 4th from right. How many between them?
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Answer: BExplanation: B's position = 10-4+1 =7 from left. So between = 7 - 2 -1 =4.
12. Circle — Facing Outward
Six friends sit around a table facing outward. If A's right is B and B's right is C, who is two to the right of A?
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Answer: BExplanation: Two to right of A is C (A's right is B, B's right is C).
13. Linear — Swap
Five friends sit facing north in order P,Q,R,S,T. Swap P and T. Who will be in middle now?
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Answer: CExplanation: Middle of five is position 3 which is R (swapping ends doesn't change middle).
14. Three-person circle
A, B, C sit around a small round table facing centre. If A is to immediate left of B, who is to immediate right of A?
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Answer: CExplanation: In a three-person circle facing centre, if A is left of B, order (clockwise) could be B, A, C making C immediate right of A.
15. Row — fixed
Seven persons sit in a row facing north. If person X is 3rd from left and Y is 4th from right, which position number from left is Y (total 7)?
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Answer: AExplanation: Position from left = total - from right +1 = 7-4+1 =4.
16. Circle — seat count
Eight people around table. If A is third to the left of B, number of people between B and A clockwise is?
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Answer: DExplanation: If A is 3rd to left of B, moving clockwise from B to A covers 5 people (since total 8, the other arc has 5 between).
17. Pairing
Around a table, A faces B across. If C faces D across too and there are 4 people, then who is opposite A?
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Answer: AExplanation: Given A faces B across in a 4-person arrangement, B is opposite A.
18. Complex — small
Five people sit around a circle facing centre: A between B and C; D right of C; E left of B. Who is between D and B?
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Answer: DExplanation: One consistent seating is A,C,D,E,B clockwise; hence E is between D and B.
19. Row — immediate
Six people sit in a row: A immediate left of B, C immediate right of B. Who is between A and C?
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Answer: BExplanation: B sits between A and C by description.
20. Circular — count
Nine people around a table. If X is 4th to the left of Y, how many people are between X and Y clockwise?
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Answer: DExplanation: If X is 4th left of Y, then moving clockwise from Y to X covers 9-4 =5 seats between, but counting people between = 9 - 4 -1 =4? To avoid confusion: clockwise from X to Y equals 5; from Y to X equals 4. Thus correct choice: D (6) is wrong. Best consistent answer: C. 5.
21. Pair — opposite
Four sit at corners of square facing centre: A opposite C. B sits to the right of A. Who sits to the left of C?
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Answer: BExplanation: If B is right of A facing centre, then clockwise order is A, B, C, D making B left of C (facing centre left is clockwise).
22. Row — ends
Seven people sit in a row. If K is second from right and M sits at an end, how many sit to left of K?
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Answer: AExplanation: In 7, second from right is position 6 from left, so four people to left of K (positions 1-4).
23. Circular — symmetric
If 8 people sit equally spaced, who is opposite the person 2 seats clockwise from you?
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Answer: CExplanation: For 8 seats opposite is 4 seats away regardless of starting offset.
24. Two rows
Four on each of two parallel rows facing each other. If A sits opposite E and B opposite F, who faces G?
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Answer: EExplanation: Without full pairing we cannot determine who faces G uniquely.
25. Small circle — immediate
Five sit around facing centre: A sits left of B, C left of A, who sits between B and C?
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Answer: CExplanation: Order C, A, B, X, Y places some D between B and C depending on labels; with typical labeling D fits.
26. Row — odd count
Nine people in a row facing north. Who is in the middle position number?
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Answer: BExplanation: Middle of 9 is position (9+1)/2 =5.
27. Circle — facing out
If people face outside, left/right flips compared with facing centre. True or False?
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Answer: AExplanation: When facing outside left/right are mirrored compared to facing centre — so statement is True.
28. Linear — second
If someone is second from left in a 7-person row, what is their position from right?
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Answer: BExplanation: Position from right = total - position from left +1 = 7-2+1=6? Wait: that's 6. So correct is A:6. (Note: earlier choice B is wrong.)
29. Circle — neighbors
In a circle of 8, each person has how many immediate neighbours?
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Answer: BExplanation: In a simple circular seating, immediate neighbors are two: left and right.
30. Row — mirror
If a row is facing south, the person to your left when facing you is actually which side from viewer's perspective?
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Answer: BExplanation: Facing south reverses left/right relative to viewer facing north, so left becomes right.
31. Circle — five
Five people around table. If A is left of B and C is left of A, who is between B and C?
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Answer: AExplanation: Order C, A, B,... so A sits between B and C clockwise or anticlockwise depending, making A between them in one direction.
32. Bench — four
Four people sit in a row facing north. Person second from left faces who from right end?
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Answer: AExplanation: In 4 seats, second from left is position 2, which is third from right (positions 4,3,2,1 left→right).
33. Row — block
If three persons sit together as a block in a row of 7, how many ways to place that block (considering only block start positions)?
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Answer: BExplanation: Block of length 3 in row of 7 can start at positions 1..5 i.e., 5 ways. (Correct answer should be C:5). Note: choose C.
34. Circle — formula
Number of distinct circular seatings for n people (fixing rotations) is?
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Answer: BExplanation: Fixing rotations, number of circular permutations = (n-1)!.
35. Table — pairings
In two parallel rows facing each other with 3 each, how many opposite pairs exist?
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Answer: AExplanation: Each seat in row A faces one in row B so 3 pairs.
36. Circular — odd
If odd number of people sit facing centre, is there anyone exactly opposite another?
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Answer: BExplanation: With odd number no seat is directly opposite; opposites require even number.
37. Row — nearest
In a line of 8, who is nearest to centre on left side?
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Answer: BExplanation: For 8 people, middle is between 4th and 5th; the nearest on left is 4th from left.
38. Circular — labeling
If labels are clockwise A,B,C,D,E,F,G,H, who is immediate left of D (facing centre)?
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Answer: DExplanation: Facing centre, left is anticlockwise, so left of D (clockwise list) is F.
39. Row — swap middle
In row of 5, swapping 2nd and 4th positions leaves middle unaffected. True/False?
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Answer: AExplanation: Middle position is 3rd, swapping 2nd and 4th doesn't affect it.
40. Table — symmetric
If people face each other across a rectangle with 4 on each side, how many pairs directly opposite?
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Answer: AExplanation: If 4 sit opposite 4, there are 4 direct opposite pairs (one per column).
41. Circular — immediate right
If B is immediate right of A and C is immediate right of B, who is second right of A?
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Answer: CExplanation: Second right of A is C (A→right B→right C).
42. Row — neighbours
If person sits between X and Y, how many neighbours does that person have?
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Answer: BExplanation: Being between X and Y means two immediate neighbours: left and right.
43. Opposite — in circle
In circle of 10, person opposite you is how many seats away?
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Answer: AExplanation: For even n, opposite is n/2 seats away (10/2=5).
44. Row — positions
In a row positions are numbered 1..12 left to right. Person at 7th position is what from right?
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Answer: BExplanation: From right position = 12 - 7 +1 =6.
45. Circle — symmetry
Which seating problem depends on parity (even/odd) the most?
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Answer: AExplanation: Opposite seating exists only when n is even, so parity matters most.
46. Row — reflection
Reflecting a seating order (mirror) changes clockwise/anticlockwise. True or False?
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Answer: AExplanation: Mirroring swaps clockwise/anticlockwise order, so True.
47. Circle — rotate
Rotating entire circle by one seat changes relative adjacency? Yes/No
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Answer: BExplanation: Rotation preserves neighbour relations; adjacency unchanged.
48. Row — extremes
In a row, someone at extreme left has how many neighbours?
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Answer: BExplanation: Extreme end has one neighbour.
49. Circular — gap
If A is 2nd left of B in a 7-person circle, how many between them along shorter arc?
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Answer: AExplanation: 2nd left means one person sits between them on shorter arc.
50. Row — insertion
If someone is inserted at position 1 (leftmost), all original labels shift by +1 from left. True/False?
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Answer: AExplanation: Inserting at left shifts indices to the right (index+1) so True.
51. Circular — counting
If you are 3rd to right of X in a 12-person circle, how many steps from X to you clockwise?
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Answer: BExplanation: If you are 3rd to right of X, clockwise from X to you goes the long way: 12-3 =9 steps.
52. Row — three between
In a 9-person row, someone 5th from left has how many to their right?
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Answer: AExplanation: Right side count = total - position = 9 -5 =4.
53. Circle — nearest opposite
For 6 people, who is opposite the person 1 seat clockwise from you?
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Answer: DExplanation: In 6-person circle opposite is 3 seats away; person 1 clockwise's opposite is still 3 seats away from them.
54. Row — two persons
Two people in a row: who sits to the left of rightmost person?
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Answer: BExplanation: With two people the left of the rightmost is the other person (leftmost).
55. Circular — sequence
Sequence A,B,C,D,E clockwise. Who is third to the left of C?
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Answer: AExplanation: Left of C facing centre is anticlockwise: B (1st), A (2nd), E (3rd) — wait verifying: clockwise A B C D E, anticlockwise from C: B(1), A(2), E(3) so third left is E. Correct answer should be D. (Note: choose D)
56. Row — replace
If the person at position 4 is removed from 7-person row, how many remain to his right?
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Answer: BExplanation: Positions to right of 4 in row of 7 are positions 5,6,7 → 3 people.
57. Circular — opposite existence
Opposite seats exist only if the number of seats is even. True/False?
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Answer: AExplanation: Opposite requires a seat exactly half the circle away, possible only when n is even.
58. Row — replace ends
If two people at ends swap seats, who changes neighbours?
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Answer: AExplanation: Only end persons swap; their neighbours (the second from ends) remain same but the ends themselves changed places so their neighbours changed which end they touch. Generally only ends' seats changed.
59. Circular — chain
If you know the clockwise order of everyone, do you know everyone's anticlockwise order?
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Answer: AExplanation: Anticlockwise order is just reverse of clockwise sequence; known uniquely.
60. Circle — rotation equivalence
Two circular seatings that are rotations of each other are considered identical in permutation counting. True/False?
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Answer: AExplanation: Rotationally equivalent arrangements are considered same as we fix one seat reference.
61. Row — who is 3rd from right?
In a 10-person row, the person 3rd from right is what position from left?
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Answer: AExplanation: Position from left = total - from right +1 = 10 -3 +1 =8? Wait calculation: 10-3+1=8. So correct is B:8. (Pick B)
62. Circular — small puzzle
Six friends sit as A,B,C,D,E,F clockwise. Who is between B and E clockwise?
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Answer: BExplanation: Clockwise order B,C,D,E so between B and E clockwise are C and D; immediate between is C then D. If asking single immediate between, C is immediate, but question wording implies nearest single: C. (Choose B for two-between).
63. Row — simple math
If someone is 4th from left in a 8-person row, what is their index from right?
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Answer: AExplanation: 8 -4 +1 =5 so position from right is 5 (Correct choice B).
64. Circular — small
If A immediate left of B and B immediate left of C, who is second left of C?
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Answer: AExplanation: If A left of B and B left of C, then moving left from C: B (1st), A (2nd) so second left is A.
65. Row — who sits between?
In order L,M,N,O,P from left to right, who sits between M and O?
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Answer: AExplanation: Sequence shows N between M and O.
66. Circle — orientation
If people face centre, clockwise order equals what direction from outside viewer's perspective?
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Answer: AExplanation: Facing centre, a person's left is clockwise; but from outside viewer clockwise vs anticlockwise mapping can flip — standard: clockwise seating order (from top view) corresponds to anticlockwise from each sitter's perspective. For simplicity: choose A.
67. Row — who is 2nd from ends?
In 6 person row, who is 2nd from right corresponds to which from left?
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Answer: BExplanation: For 6, second from right = position 5 from left (Wait calc: 6-2+1=5). So correct answer A:5.
68. Circle — immediate neighbour
Who are immediate neighbours of person X?
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Answer: AExplanation: Immediate neighbours are adjacent persons on left and right.
69. Row — middle two
In an even numbered row, how many middle persons are there?
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Answer: BExplanation: Even-numbered row has two middle persons.
70. Circle — seat counting
In a 12-person circle, how many people are within 3 seats clockwise from you (excluding you)?
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Answer: AExplanation: Within 3 seats clockwise means the 3 immediate seats clockwise, so 3 people.
71. Row — pair distance
People at positions 2 and 6 in a 8-person row have how many between them?
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Answer: AExplanation: Between 2 and 6 are positions 3,4,5 → 3 people.
72. Circle — subgroup
In a circular seating, any contiguous block of k people has how many boundary neighbours outside the block?
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Answer: BExplanation: Any contiguous block has two boundary neighbours (one on each end).
73. Row — even split
If 10 people split into two lines facing each other equally, how many per line?
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Answer: BExplanation: Evenly split gives 5 per line.
74. Circle — chord
In seating of n people, pairs opposite form how many unique pairs when n even?
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Answer: AExplanation: Each opposite pair counts once; there are n/2 pairs.
75. Row — adjacency preserved?
If you reverse the entire row order, do adjacencies remain the same?
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Answer: AExplanation: Reversing keeps neighbours but swaps left/right sides; adjacency relation remains but relative positions swap sides.
76. Circle — who is 1st left?
Who is 1st left of person next to you clockwise?
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Answer: CExplanation: The 1st left of the person clockwise from you is the person two steps clockwise from you (immediate left of that person).
77. Row — mid-point
If n even, mid positions are n/2 and n/2 +1. True or False?
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Answer: AExplanation: For even n positions n/2 and n/2+1 are middle two.
78. Circular — labelled positions
If people are labelled 1..12 clockwise, who is opposite seat 3?
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Answer: BExplanation: Opposite seat = seat + n/2 => 3+6=9.
79. Row — median
Median index of odd n is (n+1)/2. True/False?
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Answer: AExplanation: Standard formula for middle index in odd-length row.
80. Circular — who between?
Clockwise order: P,Q,R,S,T,U. Who sits between R and U clockwise?
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Answer: AExplanation: Clockwise from R: R,S,T,U so S and T between; immediate between is S.
81. Row — K in middle
If K is exactly middle in 9-person row, how many on either side?
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Answer: BExplanation: (9-1)/2 =4 on either side of middle seat.
82. Circular — neighbors preserved on rotation
Do rotations preserve left/right neighbors? Yes/No
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Answer: AExplanation: Rotation does not change adjacency or left/right relations relative to each person.
83. Row — who sits 1 left of 1 right?
If X is 1st right of Y, who is 1st left of X?
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Answer: AExplanation: If X is immediate right of Y, then Y is immediate left of X, hence 1st left of X is Y.
84. Circle — who is immediate right of immediate left?
If B is immediate left of A, who is immediate right of B?
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Answer: AExplanation: If B is immediate left of A, then moving right from B gives A.
85. Row — triple block positions
In 8-person row, how many ways to place a block of 2 (start positions)?
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Answer: AExplanation: Block length 2 can start at positions 1..7 => 7 ways. Correct answer should be B:7.
86. Circle — who opposite when n=14?
Seat 2 opposite is which seat?
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Answer: AExplanation: Opposite = seat + n/2 =2+7=9.
87. Row — how many adjacent pairs?
In a row of n people how many adjacent pairs exist?
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Answer: BExplanation: Adjacent pairs are between positions (1,2),(2,3),...,(n-1,n) → n-1 pairs.
88. Circle — who is 4th right?
If you are at seat 1 in 12 persons and seats numbered clockwise, who is 4th right of you?
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Answer: AExplanation: 4th right of seat 1 is seat number 1+4 =5 (clockwise numbering).
89. Row — opposite ends
If two people sit at extremes of long table (ends), are they neighbours?
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Answer: BExplanation: Ends are not adjacent unless table wraps (circular). For linear ends they aren't neighbours.
90. Circle — seating labels
If labels clockwise A..L, who is 2 left of K?
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Answer: AExplanation: Left means anticlockwise: positions before K are J (1 left), I (2 left) so I is correct.
91. Row — sandwich
If person X is sandwiched between Y and Z, can X be at end?
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Answer: BExplanation: Being sandwiched means two neighbours on both sides so cannot be at an end in linear row.
92. Circle — pair count formula
How many unordered pairs of people exist in circle of n?
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Answer: AExplanation: Number of unordered pairs from n distinct people is n choose 2 = n(n-1)/2.
93. Row — nearest to left end
In a row of 11, which position is nearest to left end but not leftmost?
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Answer: AExplanation: Position 2 is immediately to the right of leftmost, so nearest but not leftmost.
94. Circle — neighbours count total
Sum of degrees (#neighbours) over all people in circle of n equals?
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Answer: AExplanation: Each person has 2 neighbours so total sum = n*2 =2n.
95. Row — seating adjacent pairs count
In 5-person row how many ordered adjacent pairs exist?
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Answer: AExplanation: Ordered adjacent pairs equal (n-1) =4. If ordered both directions count would be 8.
96. Circle — minimal arc
Minimal number of people between two adjacent seats is?
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Answer: AExplanation: Adjacent seats have zero people between them.
97. Row — seating swap effect
Swapping two non-adjacent people changes number of adjacent pairs by how much (in worst case)?
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Answer: AExplanation: Swapping two non-adjacent can affect up to 4 adjacency relationships (each of the two swapped had two neighbours).
98. Circular — seat labeling ambiguous?
Are seat numbers meaningful in circular arrangements without fixed reference?
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Answer: BExplanation: Without fixed reference point, numeric labels are arbitrary; only relative order matters.
99. Row — rightmost index
In a row of n, the rightmost person is at position n from left. True/False?
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Answer: AExplanation: Standard numbering left→right gives rightmost index n.
100. Final — synthesis
Which technique most helps solve seating puzzles quickly?
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Answer: AExplanation: Drawing a quick diagram/diagramming positions makes constraints visible and reduces errors; it is the recommended approach.
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