Title: CAT 2024 Slot 3 Difficulty: Game-Based Logic Puzzle Solution
Content: English Explanation for Indian Exam aspirants
Problem Statement (Hypothetical CAT-Style Game Question):
*Five friends—A, B, C, D, and E—sit around a circular table for a game. The following conditions apply:
A sits to the immediate left of B.
C sits opposite D.
E does not sit next to C.
B does not sit next to D.
Determine the seating arrangement and identify the person sitting between A and C.*
Solution in English:
Step 1: Understand the Constraints
Circular Arrangement: Positions are relative (no fixed "start" or "end").
Key Rules:
A → B (A is immediately left of B).
C ↔ D (C and D are directly opposite each other).
E ≠ Adjacent to C.
B ≠ Adjacent to D.
Step 2: Fix Positions to Simplify
Since the table is circular, fix D’s position to avoid rotational ambiguity. Assume D is at position 1.
By Rule 2, C must be at position 3 (opposite D in a 5-seat circle).
Step 3: Place A and B Using Rule 1
A must be immediately left of B. Possible pairs (A,B) in remaining positions (2,4,5):
Option 1: A at 2, B at 3 → Conflict: B cannot be at 3 (C is there).
Option 2: A at 4, B at 5 → Valid.
Option 3: A at 5, B at 1 → Conflict: D is at 1.
Conclusion: A=4, B=5.
Step 4: Assign E Using Rule 3
Remaining position: 2.
E must not sit next to C (position 3). Adjacent to C are positions 2 and 4.
Position 2 is adjacent to C (position 3) → Conflict.
Wait—this suggests an error. Re-examine Step 3.
Revised Step 3:
If A=4, B=5, then E must go to position 2. However, E cannot sit next to C (position 3). Position 2 is adjacent to 3 → Invalid.
Alternative Option:
A=5, B=1 (but D is at 1 → Conflict).
A=2, B=3 (C is at 3 → Conflict).
Contradiction: No valid placement.
Step 5: Adjust Initial Assumption
If fixing D at 1 leads to contradiction, try fixing C at 1 (swap roles):
By Rule 2, D is at 3.
A and B must be adjacent. Remaining positions: 2,4,5.
A=2, B=3 → B cannot be at 3 (D is there).
A=4, B=5 → Valid.
Assign E to position 2 (only remaining).
E is adjacent to C (position 1) → Conflict.
Final Adjustment:
A=5, B=1 (C is at 1 → Conflict).
A=4, B=5 → E must go to 2 (adjacent to C → invalid).
Step 6: Realize Mistake in Circular Logic
In a 5-seat circle, opposite positions are two seats apart (e.g., seat 1 ↔ seat 4).
Correct Fixing: Place D at 1 → C at 4 (opposite).
A and B must be adjacent. Remaining seats: 2,3,5.
A=2, B=3 → Valid.
E=5 (not adjacent to C at 4).
Check Rule 4: B=3 is adjacent to D=1? No (seats 1 and 3 are separated by seat 5). Valid.
Final Arrangement:
1: D
2: A
3: B
4: C
5: E
Step 7: Answer the Question
Who sits between A (2) and C (4)?
Between A (2) and C (4) is seat 3 → B.
Key Takeaways for CAT Game Problems
Fix Positions Early: Break rotational symmetry by anchoring one person.
Visualize with Diagrams: Draw tables or circles to track constraints.
Test All Scenarios: If one path fails, revise assumptions (e.g., anchor different people).
Check All Rules: Ensure no constraints are violated in the final arrangement.
Answer: B sits between A and C.
Let me know if you need further clarification or additional examples!
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