The following figures are made of ovals.
- How many ovals will there be in Figure 6?
- How many ovals will there be in Figure 43?
- Which figure will have 6845 ovals?
(a)
Figure 1 = 0
2 + 1
2 = 1
Figure 2 = 1
2 + 2
2 = 5
Figure 3 = 2
2+ 3
2 = 13
Figure 4 = 3
2 + 4
2 = 25
Formula:
Number of ovals = (Figure number - 1)
2 + Figure number
2Number of ovals in Figure 6
= (6 - 1)
2 + 6
2= 5
2 + 6
2 = 5 x 5 + 6 x 6
= 61
(b)
Number of ovals in Figure 43
= (43 - 1)
2 + 43
2= 42
2 + 43
2 = 42 x 42 + 43 x 43
= 3613
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 6845
58
2 + 59
2 = 6845
Figure Number = 59
Answer(s): (a) 61; (b) 3613; (c) 59