PSLE Riordan uses toothpicks to form figures that follow a pattern. The first four figures are shown.
- 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)
- What is the difference in the number of toothpicks that Riordan would use for Figure 7 and Figure 9?
- How many toothpicks would he use for Figure 60?
(a)
Number of toothpicks used:
Figure 1: 15 = 11 + 4 x 1Figure 2: 18 = 10 + 4 x 2Figure 3: 23 = 11 + 4 x 3Figure 4: 26 = 10 + 4 x 4The 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 numberNumber 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 7 and 9 = 8
(c)
Figure 60 is an even number.
Number of toothpicks that Riordan would use for Figure 60
= 10 + 4 x Figure number
= 10 + 4 x 60
= 10 + 240
= 250
Answer(s): (a) 55, 58; (b) 8; (c) 250