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Mathematical Position Stack

Mathematical Position Stack problems involve constraints that use arithmetic operations on box positions (e.g., 'The product of positions of boxes C and D is 12', 'Box E is at a prime-numbered position'). These puzzles test arithmetic reasoning and number theory applied to stacking.

10Worksheets
200+Practice Questions
AdvancedDifficulty
3-4 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 Mathematical Position Stack

Mathematical Position Stack problems involve constraints that use arithmetic operations on box positions (e.g., 'The product of positions of boxes C and D is 12', 'Box E is at a prime-numbered position'). These puzzles test arithmetic reasoning and number theory applied to stacking.

Prerequisites

Single stack basics Arithmetic operations Prime numbers Factors and multiples Number properties
Why This Matters: Mathematical Position problems appear in 1-2 questions in advanced exams like CAT and Banking PO mains. They test arithmetic application.

How to Solve Mathematical Position Stack Problems

1

Step 1: List all positions (1 to N)

2

Step 2: Apply direct assignments

3

Step 3: Translate mathematical constraints into equations (e.g., pos(C) × pos(D) = 12)

4

Step 4: List all possible position pairs satisfying each equation

5

Step 5: Eliminate pairs that conflict with fixed positions

6

Step 6: Use elimination to determine unique arrangement

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Step 7: Answer the specific question

Pro Strategy: Create a table of positions. List all possible values for each constraint. Use elimination to narrow down possibilities. Mathematical constraints often have limited solutions.

Example Problem

Example: Boxes A-G stacked (positions 1-7). C at position 3. pos(C)×pos(D)=12. E at prime position. F at position = 5 + 2×pos(G). A+B=8, A below B. D even. G odd. Find position of A. Solution: Step 1: C=3 → D=4 (3×4=12) Step 2: Prime positions: 2,3,5,7 → E can be 2,5,7 (3 is C) Step 3: F = 5+2G → possible (G,F): (1,7) only (2→9 invalid, 3→11 invalid) Step 4: G=1, F=7 Step 5: A+B=8 with A

Pro Tips & Tricks

  • Prime positions up to 10: 2,3,5,7 (11 for larger stacks)
  • Even positions: 2,4,6,8, etc.
  • Odd positions: 1,3,5,7,9, etc.
  • Product constraints: list all factor pairs
  • Sum constraints: list all pairs that sum to given value
  • Linear equations: solve for possible integer positions

Shortcut Methods to Solve Faster

If pos(C) × pos(D) = 12, possible pairs: (1,12),(2,6),(3,4),(4,3),(6,2),(12,1)
For positions within 1-7, only (2,6),(3,4),(4,3),(6,2) are possible
Prime constraints eliminate non-prime positions immediately

Common Mistakes to Avoid

Forgetting that positions are limited to 1-N
Not listing all possible pairs for product/sum constraints
Ignoring the 'one box per position' rule
Assuming all prime positions are available (some may be taken)

Exam Importance

Mathematical Position Stack 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
0-1 questions
CAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Mathematical Position Stack?

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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