Matchstick Pattern

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.

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

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

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