The following figures are made of ovals.
- How many ovals will there be in Figure 10?
- How many ovals will there be in Figure 68?
- Which figure will have 2113 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 10
= (10 - 1)
2 + 10
2= 9
2 + 10
2 = 9 x 9 + 10 x 10
= 181
(b)
Number of ovals in Figure 68
= (68 - 1)
2 + 68
2= 67
2 + 68
2 = 67 x 67 + 68 x 68
= 9113
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 2113
32
2 + 33
2 = 2113
Figure Number = 33
Answer(s): (a) 181; (b) 9113; (c) 33
