The following figures are made of ovals.
- How many ovals will there be in Figure 6?
- How many ovals will there be in Figure 66?
- Which figure will have 6385 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 66
= (66 - 1)
2 + 66
2= 65
2 + 66
2 = 65 x 65 + 66 x 66
= 8581
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 6385
56
2 + 57
2 = 6385
Figure Number = 57
Answer(s): (a) 61; (b) 8581; (c) 57