The following figures are made of ovals.
- How many ovals will there be in Figure 5?
- How many ovals will there be in Figure 82?
- Which figure will have 3961 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 5
= (5 - 1)
2 + 5
2= 4
2 + 5
2 = 4 x 4 + 5 x 5
= 41
(b)
Number of ovals in Figure 82
= (82 - 1)
2 + 82
2= 81
2 + 82
2 = 81 x 81 + 82 x 82
= 13285
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 3961
44
2 + 45
2 = 3961
Figure Number = 45
Answer(s): (a) 41; (b) 13285; (c) 45
