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.

10Worksheets
200+Practice Questions
AdvancedDifficulty
3-4 hoursHours to Master

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

Constraint satisfaction Multiple solution analysis Necessary vs possible Assignment problems
Why This Matters: Multi-Person Deduction problems appear in 1-2 questions in Banking PO mains and CAT. They test logical necessity and constraint analysis.

How to Solve Dynamic Multi-Person Deduction Problems

1

Step 1: List all persons and tasks/roles

2

Step 2: Apply all given constraints

3

Step 3: Enumerate all valid assignments (or reason systematically)

4

Step 4: For each person-task pair, check if it appears in all valid assignments

5

Step 5: If yes, that assignment is forced (must be true)

6

Step 6: Answer which statement must be true

Pro Strategy: Find all possible valid configurations. An assignment is forced only if it occurs in every valid configuration. Use systematic case analysis.

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

If only one valid configuration exists, all assignments are forced
If a constraint eliminates all but one possibility for a person, that's forced
Check contradictions: if assumption leads to invalid, opposite must be true

Common Mistakes to Avoid

Confusing 'possible' with 'must be true'
Assuming a configuration is valid without checking all constraints
Not considering all possible valid configurations
Missing that multiple valid configurations may exist

Exam Importance

Dynamic Multi-Person Deduction is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
2-3 questions
RAILWAYS RRB
0-1 questions
CAT
2-3 questions
INSURANCE
1-2 questions

Ready to Master Dynamic Multi-Person Deduction?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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