The diagram shows toothpicks used to arrange the following patterns. The rest of the figures follow the same pattern.
Figure 1 uses 4 toothpicks.
Figure 2 uses 10 toothpicks.
Figure 3 uses 18 toothpicks.
- How many squares are in Figure 9?
- How many toothpicks are used to make Figure 42?
(a)
Number of squares:
Figure
1:
1 Figure
2: 1 +
2 = 3
Figure
3: 1 + 2 +
3 = 6
Last digit in the list = Figure Number
Formula:
Number of squares =
Figure No x (Figure No + 1)2 Number of squares in Figure 9
= 1 + 2 + 3 + ... + 7 + 8 + 9
=
9 x 102 = 45
(b)
Number of toothpicks:
Figure
1: 4 =
1 x
4 Figure
2: 10 =
2 x
5 Figure
3: 18 =
3 x
6 Formula:
Number of toothpicks =
Figure number x
(Figure number + 3) Number of toothpicks used to make Figure 42
= 42 x (42 + 3)
= 42 x 45
= 1890
Answer(s): (a) 45; (b) 1890