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CISCEICSE ICSE Class 6
पाठ्यपुस्तक उत्तरे९५२२
संकल्पना स्पष्टीकरण आणि व्हिडिओ३०७
अभ्यासक्रम

Matchstick Pattern

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Topics

  • Introduction
  • Matchstick Pattern Rule
  • Examples
  • Key points Summary
CISCE: Class 6

Introduction

A matchstick pattern is a way of building shapes using matchsticks, where each new figure follows a specific rule.

In this topic, we learn how to create connected squares and find out exactly how many matchsticks we need for any figure number.

CISCE: Class 6

Matchstick Pattern Rule

Step-by-step derivation:

  1. The first figure has 4 matchsticks.
  2. Each new figure adds 3 matchsticks.
  3. For figure number n: M = 4 + 3 × (n − 1)
  4. Let's simplify: M = 4 + 3n − 3 = 3n + 1
Figure Number (n) Number of Matchsticks(M)
1 4
2 7
3 10
4 13

Therefore, our formula is
M = 3n + 1
Where: M = total matchsticks, n = figure number

CISCE: Class 6

Examples

1. For the 10th figure:

  • M = 3n + 1

  • M = 3 × 10 + 1
        = 31 matchsticks

2. For the 100th figure:

  • M = 3n + 1
  • M = 3 × 100 + 1
         = 301 matchsticks

3. Which figure needs 25 matchsticks?

  • 25 = 3n + 1
  • 24 = 3n
  • n = 8, so it's Figure 8
CISCE: Class 6

Key Points Summary

Pattern Type Matchstick Pattern (Connected Squares)
Formula M = 3n + 1
First Term 4 matchsticks
Common Difference 3 matchsticks
Sequence Type Arithmetic Sequence
Key Concept Sharing sides saves matchsticks

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