The following figures are made of ovals.
- How many ovals will there be in Figure 6?
- How many ovals will there be in Figure 33?
- Which figure will have 2665 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 33
= (33 - 1)
2 + 33
2= 32
2 + 33
2 = 32 x 32 + 33 x 33
= 2113
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 2665
36
2 + 37
2 = 2665
Figure Number = 37
Answer(s): (a) 61; (b) 2113; (c) 37
