The following figures are made of ovals.
- How many ovals will there be in Figure 9?
- How many ovals will there be in Figure 36?
- Which figure will have 6161 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 9
= (9 - 1)
2 + 9
2= 8
2 + 9
2 = 8 x 8 + 9 x 9
= 145
(b)
Number of ovals in Figure 36
= (36 - 1)
2 + 36
2= 35
2 + 36
2 = 35 x 35 + 36 x 36
= 2521
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 6161
55
2 + 56
2 = 6161
Figure Number = 56
Answer(s): (a) 145; (b) 2521; (c) 56