Dynamic Multi-Person Deduction
Dynamic Multi-Person Deduction problems involve assigning people to tasks or roles with multiple constraints. You must determine which assignments are forced (must be true in all valid solutions) by analyzing all possible valid configurations.
What You'll Learn
Introduction to Dynamic Multi-Person Deduction
Dynamic Multi-Person Deduction problems involve assigning people to tasks or roles with multiple constraints. You must determine which assignments are forced (must be true in all valid solutions) by analyzing all possible valid configurations.
Prerequisites
How to Solve Dynamic Multi-Person Deduction Problems
Step 1: List all persons and tasks/roles
Step 2: Apply all given constraints
Step 3: Enumerate all valid assignments (or reason systematically)
Step 4: For each person-task pair, check if it appears in all valid assignments
Step 5: If yes, that assignment is forced (must be true)
Step 6: Answer which statement must be true
Example Problem
Example: 4 people (A,B,C,D) assigned to 4 tasks (1,2,3,4). A does task 1. B cannot do task 4. C and D are consecutive in task order. Which must be true? Solution: Step 1: Task order: 1→2→3→4 Step 2: A at task 1 (fixed) Step 3: B not at task 4 Step 4: C and D consecutive (positions differ by 1) Step 5: Enumerate possibilities: remaining tasks 2,3,4 for B,C,D Step 6: C and D consecutive means (2,3) or (3,4) in some order Step 7: B cannot be 4, so B must be 2 or 3 Step 8: In all valid assignments, some forced relationships emerge Answer: [Statement that is always true]
Pro Tips & Tricks
- Start with fixed assignments
- List all possible positions for each person
- Use process of elimination to reduce possibilities
- If a person can only be in one position across all cases, that's forced
- If a task can only be done by one person across all cases, that's forced
- Draw possibility tables
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Dynamic Multi-Person Deduction. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Dynamic Multi-Person Deduction is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Dynamic Multi-Person Deduction?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: