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Number Pyramids

Number Pyramid problems present numbers arranged in a triangular pyramid where each number is derived from the numbers below it (or above it). Common operations include addition (each cell is sum of the two below) or multiplication. These problems test your ability to work with hierarchical patterns.

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 Number Pyramids

Number Pyramid problems present numbers arranged in a triangular pyramid where each number is derived from the numbers below it (or above it). Common operations include addition (each cell is sum of the two below) or multiplication. These problems test your ability to work with hierarchical patterns.

Prerequisites

Basic addition and multiplication Hierarchical structure understanding Working from bottom up Pattern extrapolation
Why This Matters: Number Pyramid problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test hierarchical pattern recognition.

How to Solve Number Pyramids Problems

1

Step 1: Identify the pyramid structure (number of levels)

2

Step 2: Determine the rule (addition: each cell = sum of two below)

3

Step 3: Or multiplication: each cell = product of two below

4

Step 4: Work from the base upward to find missing values

5

Step 5: For top-down pyramids, work from top downward

6

Step 6: Verify all calculations are consistent

7

Step 7: Answer the specific question (missing value, top value, etc.)

Pro Strategy: Start from the known base (bottom row) and work upward applying the operation. For missing base values, work downward from known top values. Addition pyramids are more common than multiplication pyramids.

Example Problem

Example: Pyramid base: 2, 4, 6. Each upper cell is sum of two below. Find top value. Solution: Step 1: Base: 2, 4, 6 Step 2: Level 2: 2+4=6, 4+6=10 Step 3: Level 3 (top): 6+10=16 Answer: 16

Pro Tips & Tricks

  • Addition pyramid: each cell = sum of two directly below
  • Multiplication pyramid: each cell = product of two below
  • The top number is the sum of all base numbers (for addition pyramid with binomial coefficients)
  • The top number in addition pyramid = Σ(base × binomial coefficient)
  • For base length n, top = sum of (base[i] × C(n-1, i-1))
  • Work systematically from known values

Shortcut Methods to Solve Faster

For addition pyramid, top = sum of (base[i] × combination)
For 3-level pyramid: top = base[1] + 2×base[2] + base[3]
For 4-level pyramid: top = base[1] + 3×base[2] + 3×base[3] + base[4]
Multiplication pyramids are less common but follow similar pattern

Common Mistakes to Avoid

Adding wrong cells together
Working from top down when base is given
Forgetting that each level has one fewer element
Misidentifying which cells combine

Exam Importance

Number Pyramids 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
2-3 questions
INSURANCE
1-2 questions

Ready to Master Number Pyramids?

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

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now