The following figures are made of ovals.
- How many ovals will there be in Figure 9?
- How many ovals will there be in Figure 77?
- Which figure will have 6613 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 9
= (9 - 1)
2 + 9
2= 8
2 + 9
2 = 8 x 8 + 9 x 9
= 145
(b)
Number of ovals in Figure 77
= (77 - 1)
2 + 77
2= 76
2 + 77
2 = 76 x 76 + 77 x 77
= 11705
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 6613
57
2 + 58
2 = 6613
Figure Number = 58
Answer(s): (a) 145; (b) 11705; (c) 58