Each of the figures is made up of 1-cm toothpicks.
The table shows the number of toothpicks used to make the figures and their perimeters.

1. Find the number of toothpicks in Figure 20.
2. What is the perimeter of Figure 50?
3. Which figure requires a total number of 3103 toothpicks?

(a)
Pattern for the number of toothpicks
Figure 1: 1 x 8 + 7 = 15
Figure 2: 2 x 8 + 7 = 23
Figure 3: 3 x 8 + 7 = 31

Formula:
Number of toothpicks = Pattern number x 8 + 7

Number of toothpicks in Figure 20
= 20 x 8 + 7
= 167

(b)
Pattern for the perimeter of the figure
Figure 1 = 1 x 2 + 7 = 9
Figure 2 = 2 x 2 + 7 = 11
Figure 3 = 3 x 2 + 7 = 13

Formula:
Perimeter of the figure = Pattern number x 2 + 7

Perimeter of figure 50
= 50 x 2 + 7
= 107

(c)
Figure number x 8 + 7 = 3103
Figure number x 8 = 3103 - 7 = 3096
Figure number = 3096 ÷ 8 = 387

Answer(s): (a) 167; (b) 107; (c) 387