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Complex Scenarios: Vacant Floors

Vacant Floors puzzles involve a building where some floors have no occupants. The number of people is less than the total number of floors. You must determine which floors are vacant while arranging the people on the occupied floors using gap constraints that count empty floors as entities between people.

10Worksheets
200+Practice Questions
AdvancedDifficulty
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 Complex Scenarios: Vacant Floors

Vacant Floors puzzles involve a building where some floors have no occupants. The number of people is less than the total number of floors. You must determine which floors are vacant while arranging the people on the occupied floors using gap constraints that count empty floors as entities between people.

Prerequisites

Basic floor arrangement skills Handling of empty positions Gap counting including empty floors Positional deduction
Why This Matters: Vacant Floors puzzles appear in 1-2 questions in Banking PO mains and SSC CGL exams. They test handling of empty positions and gap counting with vacancies.

How to Solve Complex Scenarios: Vacant Floors Problems

1

Step 1: Determine total floors (N) and number of people (M), with N > M

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Step 2: Identify vacant floors from given clues or deduce them

3

Step 3: Place all directly given people at their specified floors

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Step 4: Apply gap constraints: empty floors count as entities between people

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Step 5: Use process of elimination to determine occupied and vacant floors

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Step 6: Answer the specific question (e.g., sum of vacant floor numbers, which floor is vacant)

Pro Strategy: Empty floors are 'entities' when counting floors between people. If exactly k entities between X and Y, then |floor(X) - floor(Y)| = k+1. Use equations to find vacant floor positions.

Example Problem

Example: 8 floors (1-8), 6 people. Floor 4 is vacant. Exactly two floors between A and B. C lives on floor 7. D lives immediately above E. Find vacant floors. Solution: Step 1: Floors 1-8, vacant floors = 8-6 = 2 vacant floors Step 2: Floor 4 is vacant (given) Step 3: C at floor 7 Step 4: Exactly two floors between A and B → |A-B| = 3 Step 5: D immediately above E → consecutive, D above E Step 6: Identify second vacant floor by elimination Answer: Vacant floors determined

Pro Tips & Tricks

  • Empty positions count as 'entities' when counting floors between
  • If exactly k entities between X and Y, then |pos(X) - pos(Y)| = k+1
  • Total floors = number of people + number of vacant floors
  • Vacant floors can be anywhere unless constrained
  • Use variables for number of people above/below vacant floors
  • Solve equations to find vacant floor positions

Shortcut Methods to Solve Faster

Number of vacant floors = total floors - number of people
If exactly k entities between X and Y, and both are occupied, the gap includes empty floors
The sum of vacant floor numbers can be found by subtracting sum of occupied floors from total sum
Total sum of floors = N(N+1)/2

Common Mistakes to Avoid

Forgetting that empty floors count as entities in gap calculations
Assuming vacant floors are consecutive
Not considering that vacant floors can be at ends
Miscounting entities between positions

Exam Importance

Complex Scenarios: Vacant Floors 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
0-1 questions
INSURANCE
1-2 questions

Ready to Master Complex Scenarios: Vacant Floors?

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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