PSLE
Pierre 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 10 and Figure 11. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Pierre would use for Figure 9 and Figure 13?
3. How many toothpicks would he use for Figure 39?

; (c) 166
(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 10
= 10 + 4 x 10 
= 10 + 40
= 50

Number of toothpicks used for Figure 11
= 11 + 4 x 11
= 11 + 44
= 55

(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 39 is an odd number.

Number of toothpicks that Pierre would use for Figure 39
= 11 + 4 x Figure number
= 11 + 4 x 39
= 11 + 156
= 167

Answer(s): (a) 50, 55; (b) 16; (c) 167