The diagram shows toothpicks used to arrange the following patterns. The rest of the figures follow the same pattern.
Figure 1 uses 18 toothpicks.
Figure 2 uses 28 toothpicks.
Figure 3 uses 40 toothpicks.
- How many squares are in Figure 8?
- How many toothpicks are used to make Figure 67?
(a)
Number of squares:
Figure
1: 1 + 2 +
3 = 6
Figure
2: 1 + 2 + 3 +
4 = 10
Figure
3: 1 + 2 + 3 + 4 +
5 = 15
Last digit in the list =
Figure number + 2 Formula:
Number of squares =
(Figure No + 2) x (Figure No + 3)2 Number of squares in Figure 8
= 1 + 2 + 3 + ... + 8 + 9 + 10
=
10 x 112 = 55
(b)
Number of toothpicks:
Figure
1: 18 =
3 x
6 Figure
2: 28 =
4 x
7 Figure
3: 40 =
5 x
8 Formula:
Number of toothpicks =
(Figure number + 2) x
(Figure number + 5) Number of toothpicks used to make Figure 67
= (67 + 2) x (67 + 5)
= 69 x 72
= 4968
Answer(s): (a) 55; (b) 4968