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Mixed Puzzle (Combination)

Introduction

The Mixed Puzzle (Combination) pattern combines two or more basic puzzle types - for example, seating + professions, floor + months, or table + colors - into a single multi-layered logic problem.

This pattern is important because exam-style problems often combine patterns to increase cognitive load: you must manage multiple attributes (position, direction, category) simultaneously while preserving all constraints.

Pattern: Mixed Puzzle (Combination)

Pattern

Combine two or more arrangement types (seating, floor, tabular attributes) and solve by progressive elimination and cross-referencing.

Typical steps: (1) identify fixed pairs/blocks, (2) convert directional clues into offsets, (3) build a multi-attribute grid (partial matrix), and (4) eliminate until all attributes fit.

Step-by-Step Example

Question

Eight people - A, B, C, D, E, F, G, H - sit around a circular table facing the center. Each person also belongs to a different department: HR, IT, Finance, Sales, Ops, Legal, R&D, Marketing. Clues:

  1. A sits third to the right of D.
  2. The HR person sits opposite the Finance person.
  3. C is immediate left of the IT person.
  4. G sits between the Sales and R&D persons.
  5. H is two seats clockwise from the Marketing person.
Who sits opposite the IT person?

Options:
A) A    B) B    C) C    D) E

Solution

  1. Step 1: Place a reference

    Place D at an arbitrary seat to break rotational symmetry; we will index seats clockwise from that reference.

  2. Step 2: Apply the A-D offset

    A sits third to the right of D. Facing the center, right = clockwise → from D move three seats clockwise to place A.

  3. Step 3: Fix HR ↔ Finance opposite pair

    Opposite in an 8-seat circle = 4 seats apart. Place HR and Finance in opposite seats (n and n+4). In this arrangement choose HR at seat 8 and Finance at seat 4 to satisfy future placements.

  4. Step 4: Place IT & its left neighbor

    C is immediate left of the IT person (left = anticlockwise). Place C and IT as an adjacent pair (C anticlockwise of IT).

  5. Step 5: Place G between Sales & R&D and Marketing-H offset

    Put a contiguous triple Sales - G - R&D (G between Sales and R&D). Also place Marketing and H so that H is two seats clockwise from Marketing (Marketing → +2 → H).

  6. Step 6: Complete by elimination

    Filling remaining departments and people by elimination gives one consistent arrangement (clockwise seats 1→8 shown below). Verify all clues against this table.
    Seat (clockwise)PersonDepartment
    1BR&D
    2GOps
    3ASales
    4EFinance
    5FMarketing
    6CLegal
    7HIT
    8DHR

  7. Final Answer:

    A → Option A

  8. Quick Check:

    A is 3rd right of D (Seat 3 vs Seat 8) ✅ HR (D seat 8) opposite Finance (E seat 4) ✅ C immediate left of IT (C seat 6 left of H seat 7) ✅ G between Sales (seat 3) & R&D (seat 1) ✅ H is two seats clockwise from Marketing (Marketing seat 5 → H seat 7) ✅

Quick Variations

1. Combine circle + ages (seating + numeric comparisons).

2. Floor (vertical) + professions (multi-attribute table).

3. Seating + timetable (day/time slots + attributes).

4. Mixed puzzles with one or more "not adjacent" constraints to increase elimination complexity.

Trick to Always Use

  • Step 1: Place opposites and absolute offsets first (they reduce symmetry).
  • Step 2: Convert left/right into clockwise index moves to avoid confusion.
  • Step 3: Maintain a partial matrix (seat ↔ person ↔ attribute) and iterate by elimination.

Summary

Summary

  • Lock fixed/opposite pairs first to reduce symmetric permutations.
  • Translate directional clues into seat offsets (use +clockwise indices).
  • Place contiguous blocks (e.g., X between Y & Z) as single units during placement.
  • Always verify opposites using the rule: opposite seat = n ± 4 (mod 8) for 8-person circles.

Example to remember:
Fix opposites/absolute offsets first, then place adjacent pairs and contiguous blocks, and finally fill remaining attributes by elimination.

Practice

(1/5)
1. Six colleagues - A, B, C, D, E, and F - sit in a row facing north. A is third from the left. B sits immediately right of C. D sits at an extreme end. E sits immediately left of F. Who sits fourth from the left?
easy
A. E
B. F
C. B
D. C

Solution

  1. Step 1: Place absolute spot

    A is 3rd from left → positions (left→right): [_ , _ , A , _ , _ , _].

  2. Step 2: Place adjacency blocks

    B immediate right of C → block [C B]. E immediate left of F → block [E F]. D must occupy pos1 or pos6 (an end).

    3. Step 3: Fit the blocks

    One arrangement that satisfies all constraints is: C, B, A, E, F, D (left→right). That makes 4th from left = E.

  3. Final Answer:

    E → Option A

  4. Quick Check:

    A at 3 ✅ [C B] & [E F] placed ✅ D at an end ✅
Hint: Place fixed absolute positions first, then fit adjacency blocks around them.
Common Mistakes: Placing adjacency blocks before honouring fixed absolute positions.
2. Five students - P, Q, R, S, and T - sit in a row (left to right). Clues: (1) The Physics student sits at the left end. (2) Q sits immediately right of T. (3) The Biology student sits immediately left of R. (4) P sits immediately left of R. (5) The Chemistry student sits at the right end. Who studies Biology?
easy
A. Q
B. P
C. R
D. S

Solution

  1. Step 1: Fix end subjects

    Physics = left end (pos1). Chemistry = right end (pos5).

  2. Step 2: Note adjacency blocks

    Q is immediately right of T → [T Q]. P is immediately left of R → [P R]. The Biology student sits immediately left of R → [Biology, R].

    3. Step 3: Combine (P left of R) and (Biology left of R)

    Both clues (3) and (4) imply the same left-of-R seat: the person immediately left of R is the Biology student and also is P. Therefore P = Biology. A consistent seating (left→right) example: T (Physics), Q, P (Biology), R, S (Chemistry).

  3. Final Answer:

    P → Option B

  4. Quick Check:

    Physics left end ✅ Q immediately right of T ✅ P immediately left of R and is Biology ✅ Chemistry right end ✅
Hint: If two clues point to 'person immediately left of X', they identify the same seat - combine them to deduce identity.
Common Mistakes: Not recognising that two separate 'immediately left of R' clues refer to the same seat.
3. Five colleagues - P, Q, R, S, T - have unique devices (Laptop, Tablet, Phone, Desktop, Watch) and shifts (Morning, Mid, Afternoon, Evening, Night). Clues: 1) P works Morning and does not use Phone. 2) The Tablet user works before the Phone user. 3) Q uses Desktop. 4) The Watch user works after the Tablet user but before Night. 5) R works Afternoon. Who uses the Phone?
easy
A. S
B. T
C. Q
D. R

Solution

  1. Step 1: Fix known shifts and devices

    The shifts in order are Morning, Mid, Afternoon, Evening, Night. From the clues: P = Morning (and P ≠ Phone), R = Afternoon, Q = Desktop.

  2. Step 2: Locate the Watch user

    Clue 4: Watch is after Tablet and before Night. The Watch shift must therefore be either Afternoon (3) or Evening (4). Since R = Afternoon, assign Watch = Afternoon → R = Watch.

  3. Step 3: Place Tablet and Phone (Tablet before Phone)

    Clue 2 now requires Tablet earlier than Phone. With Afternoon taken by Watch, the only feasible slots that keep Tablet before Phone and still allow Watch to be after Tablet are: Tablet = Mid (2) and Phone = Evening (4). So assign Tablet → Mid and Phone → Evening.

  4. Step 4: Assign remaining people & devices

    Used slots/devices so far: Morning (P, not Phone), Mid (Tablet, person left), Afternoon (R, Watch), Evening (Phone, person left), Night (Q, Desktop). Remaining persons: T and S. Remaining devices: Laptop and Phone (but Phone assigned to Evening). P must be Laptop (Morning). Therefore Mid (Tablet) = T and Evening (Phone) = S. Night = Q (Desktop).

  5. Step 5: Final Table

    ShiftPersonDevice
    MorningPLaptop
    MidTTablet
    AfternoonRWatch
    EveningSPhone
    NightQDesktop

  6. Final Answer:

    S → Option A

  7. Quick Check:

    P = Morning and not Phone ✅ Tablet (Mid) before Phone (Evening) ✅ Watch (Afternoon) after Tablet and before Night ✅ Q = Desktop at Night ✅
Hint: Place fixed shifts first, assign the 'after/before' chain for devices, then fill remaining people by elimination.
Common Mistakes: Interpreting 'before' as 'immediately before' (consecutive) when the puzzle requires only an earlier shift.
4. Four people - J, K, L, M - occupy four consecutive floors (1 = lowest to 4 = highest). Clues: (1) M lives on the top floor. (2) K lives on the lowest floor. (3) J is the Designer and does not live on floor 1 or 4. (4) The Designer lives immediately above the Tester. Who is the Tester?
medium
A. J
B. K
C. L
D. M

Solution

  1. Step 1: Fix extremes

    M = floor 4 (top), K = floor 1 (lowest).

  2. Step 2: Place J

    J is Designer and cannot be on 1 or 4, so J must be on floor 2 or 3. Because Designer is immediately above the Tester, Designer cannot be on floor 2 (that would put Tester on floor 1 but K already occupies floor 1). So J must be on floor 3 and thus is Designer.

  3. Step 3: Determine Tester

    Designer on 3 implies Tester is on 2. The only person left for floor 2 is L. Hence Tester = L.

  4. Final Answer:

    L → Option C

  5. Quick Check:

    M=4 & K=1 fixed ✅ J (Designer) at 3 not at extremes ✅ Designer immediately above Tester (3 above 2) ✅
Hint: If extremes are fixed, 'not on 1 or 4' pins the only middle candidate, enabling the Designer→Tester pair placement.
Common Mistakes: Placing Designer on floor 2 without checking whether floor 1 is already occupied.
5. Eight persons sit around a circular table facing the center. Departments: HR, Finance, Sales, IT, R&D, Ops, Legal, Marketing. Clues: (1) D is opposite E. (2) HR and Finance are opposite. (3) A is third to the right of D. (4) C sits immediately left of the IT head. (5) The Sales head sits adjacent to HR. Who is opposite the IT head?
medium
A. A
B. H
C. E
D. F

Solution

  1. Step 1: Fix opposite pairs

    Place D and E opposite; place HR opposite Finance (fixed 4-seat gap).

  2. Step 2: Place A relative to D

    A is third to the right of D (clockwise, since facing center) - this fixes A's seat relative to D.

  3. Step 3: Place C & IT and Sales adjacency

    C is immediately left (anticlockwise) of IT head. Sales sits next to HR. Filling these neighbors consistently around the locked opposites yields a unique arrangement where the person opposite IT is F.

  4. Final Answer:

    F → Option D

  5. Quick Check:

    D opposite E ✅ HR opposite Finance ✅ A third right of D satisfied ✅ C left of IT satisfied ✅ Sales adjacent to HR satisfied ✅
Hint: Lock opposite pairs first; then place multi-step offsets such as 'third to the right' before filling neighbors.
Common Mistakes: Mixing clockwise and anticlockwise when people face the center.

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