Matchstick Patterns

Let's solve the following problem:

Matchstick Patterns

 

Step 1

We count that 4 matchsticks are needed for the arrangement in figure №1.

For the arrangement in figure №2, 3 more matchsticks have been added. From which it follows that for each subsequent figure 3 sticks are needed.

Step 2

Solution:

For the first figure -> 4 matchsticks
For the remaining 21 figures -> 21 x 4 matchsticks

(1 x 4) + (21 x 3) = 4 + 63 = 67

Answer: 67 matches