PSLE Ethan 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 5 and Figure 6. Give your answers in numbers. (Eg 1, 2)
- What is the difference in the number of toothpicks that Ethan would use for Figure 19 and Figure 21?
- How many toothpicks would he use for Figure 58?
(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 5
= 11 + 4 x 5
= 11 + 20
= 31
Number of toothpicks used for Figure 6
= 10 + 4 x 6
= 10 + 24
= 34
(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 19 and 21 = 8
(c)
Figure 58 is an even number.
Number of toothpicks that Ethan would use for Figure 58
= 10 + 4 x Figure number
= 10 + 4 x 58
= 10 + 232
= 242
Answer(s): (a) 31, 34; (b) 8; (c) 242
