The diagram shows toothpicks used to arrange the following patterns. The rest of the figures follow the same pattern.
Figure 1 uses 10 toothpicks.
Figure 2 uses 18 toothpicks.
Figure 3 uses 28 toothpicks.
- How many squares are in Figure 14?
- How many toothpicks are used to make Figure 82?
(a)
Number of squares:
Figure
1: 1 +
2 = 3
Figure
2: 1 + 2 +
3 = 6
Figure
3: 1 + 2 + 3 +
4 = 10
Last digit in the list =
Figure number + 1 Formula:
Number of squares =
(Figure No + 1) x (Figure No + 2)2 Number of squares in Figure 14
= 1 + 2 + 3 + ... + 13 + 14 + 15
=
15 x 162 = 120
(b)
Number of toothpicks:
Figure
1: 10 =
2 x
5 Figure
2: 18 =
3 x
6 Figure
3: 28 =
4 x
7 Formula:
Number of toothpicks =
(Figure number + 1) x
(Figure number + 4) Number of toothpicks used to make Figure 82
= (82 + 1) x (82 + 4)
= 83 x 86
= 7138
Answer(s): (a) 120; (b) 7138