PSLE
Daniel 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 11 and Figure 12. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Daniel would use for Figure 17 and Figure 19?
3. How many toothpicks would he use for Figure 56?

(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 11
= 11 + 4 x 11 
= 11 + 44
= 55

Number of toothpicks used for Figure 12
= 10 + 4 x 12
= 10 + 48
= 58

(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 17 and 19 = 8

(c)
Figure 56 is an even number.

Number of toothpicks that Daniel would use for Figure 56
= 10 + 4 x Figure number
= 10 + 4 x 56
= 10 + 224
= 234

Answer(s): (a) 55, 58; (b) 8; (c) 234