PSLE
Warren 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 6 and Figure 7. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Warren would use for Figure 9 and Figure 13?
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 6
= 10 + 4 x 6 
= 10 + 24
= 34

Number of toothpicks used for Figure 7
= 11 + 4 x 7
= 11 + 28
= 39

(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 9 and 13
= 2 x 8
= 16

(c)
Figure 23 is an odd number.

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

Answer(s): (a) 34, 39; (b) 16; (c) 103