PSLE
Caden 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 4 and Figure 5. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Caden would use for Figure 18 and Figure 22?
3. How many toothpicks would he use for Figure 23?

; (c) 102
(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 4
= 10 + 4 x 4 
= 10 + 16
= 26

Number of toothpicks used for Figure 5
= 11 + 4 x 5
= 11 + 20
= 31

(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 18 and 22
= 2 x 8
= 16

(c)
Figure 23 is an odd number.

Number of toothpicks that Caden would use for Figure 23
= 11 + 4 x Figure number
= 11 + 4 x 23
= 11 + 92
= 103

Answer(s): (a) 26, 31; (b) 16; (c) 103