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Min/Max Persons in Row

Min/Max Persons problems ask for the minimum or maximum possible number of persons in a row given certain rank constraints. These problems test your ability to find bounds and optimize under given conditions. You must consider the worst-case and best-case scenarios for arrangement.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Min/Max Persons in Row

Min/Max Persons problems ask for the minimum or maximum possible number of persons in a row given certain rank constraints. These problems test your ability to find bounds and optimize under given conditions. You must consider the worst-case and best-case scenarios for arrangement.

Prerequisites

Position from one side concepts Understanding of rank constraints Optimization thinking Bound calculation
Why This Matters: Min/Max Persons problems appear in 1-2 questions in Banking PO and SSC CGL exams. They test optimization and bound reasoning.

How to Solve Min/Max Persons in Row Problems

1

Step 1: Identify all rank constraints given

2

Step 2: For minimum total, arrange persons as compactly as possible (overlap positions)

3

Step 3: For maximum total, arrange persons as spread out as possible

4

Step 4: Use the fact that the same person cannot occupy two positions

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Step 5: Calculate the minimum possible total = maximum of the required positions

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Step 6: For maximum, there is often no upper bound unless specified

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Step 7: Present the answer

Pro Strategy: For minimum total, try to make persons overlap as much as possible. The minimum is the maximum of the constraints. For maximum total, arrange persons at extremes; often unbounded.

Example Problem

Example: In a row, A is 8th from left and B is 12th from right. What is the minimum number of persons in the row? Solution: Step 1: A's left rank = 8, B's right rank = 12 Step 2: Minimum occurs when A and B overlap or are the same person Step 3: Minimum total = max(8, 12) = 12 Answer: 12 persons

Pro Tips & Tricks

  • Minimum total = max(all constraints that give lower bounds)
  • If two persons are given, minimum = max(L1, R2)
  • If persons are on the same side, minimum = larger rank
  • Maximum is often unbounded unless specific conditions exist
  • For three persons, minimum = max of all positional requirements

Shortcut Methods to Solve Faster

For two persons: Min = max(L1, R2) if one from left, one from right
For same side: Min = max(L1, L2)
Max total is usually infinite unless bounded by other conditions

Common Mistakes to Avoid

Assuming maximum is always bounded
Not considering that persons could be the same
Using sum instead of max for minimum calculation

Exam Importance

Min/Max Persons in Row is an important topic for various competitive exams. Here's how frequently it appears:

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

Ready to Master Min/Max Persons in Row?

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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