Irene added a certain number of white squares round a grey square and then a certain number of grey squares round the white squares and she continued adding more grey and white squares round the diagram in each pattern as shown.

1. How many grey squares did she need if the most outer layer had 9 squares on each side?
2. How many squares are there in the Figure 14?

(a)
Formula:
Number of squares on each side = Figure number x 2 - 1

Figure number x 2 - 1 = 9
Figure number x 2 = 9 + 1 = 10
Figure number = 10 ÷ 2 = 5

Pattern for the total number of squares
Figure 1: 1 x 1 = 1 square
Figure 2: 3 x 3 = 9 squares
Figure 3: 5 x 5 = 25 squares

Formula:
Total number of squares = [(Figure number x 2) - 1]²

Total number of squares at Figure 5 = [(5 x 2) - 1]²
= 9 x 9
= 81

Number of white squares at Figure 5 = 32 (Same as Figure 4)

Number of grey squares at Figure 5
= Total number of squares at Figure 5 - Number of white squares at Figure 5
= 81 - 32
= 49

(b)
Total number of squares at Figure 14
= [(14 x 2) - 1]²
= 27 x 27
= 729

Answer(s): (a) 49; (b) 729