The following figures are made of ovals.
- How many ovals will there be in Figure 8?
- How many ovals will there be in Figure 37?
- Which figure will have 5941 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 8
= (8 - 1)
2 + 8
2= 7
2 + 8
2 = 7 x 7 + 8 x 8
= 113
(b)
Number of ovals in Figure 37
= (37 - 1)
2 + 37
2= 36
2 + 37
2 = 36 x 36 + 37 x 37
= 2665
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 5941
54
2 + 55
2 = 5941
Figure Number = 55
Answer(s): (a) 113; (b) 2665; (c) 55
