PSLE
Vaidev uses toothpicks to form figures that follow a pattern. The first four figures are shown.

1. The table shows the number of toothpicks used for each figure. Complete the table for Figure 9 and Figure 10. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Vaidev would use for Figure 16 and Figure 18?
3. How many toothpicks would he use for Figure 30?

(a)
Number of toothpicks used:
Figure 1: 15 = 11 + 4 x 1
Figure 2: 18 = 10 + 4 x 2
Figure 3: 23 = 11 + 4 x 3
Figure 4: 26 = 10 + 4 x 4

The formula for the total number of toothpicks used is different for odd-numbered patterns and even-numbered patterns.
Number of toothpicks for odd-numbered figure = 11 + 4 x Figure number
Number of toothpicks for even-numbered figure = 10 + 4 x Figure number

Number of toothpicks used for Figure 9
= 11 + 4 x 9 
= 11 + 36
= 47

Number of toothpicks used for Figure 10
= 10 + 4 x 10
= 10 + 40
= 50

(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 16 and 18 = 8

(c)
Figure 30 is an even number.

Number of toothpicks that Vaidev would use for Figure 30
= 10 + 4 x Figure number
= 10 + 4 x 30
= 10 + 120
= 130

Answer(s): (a) 47, 50; (b) 8; (c) 130