Natalie 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.
- How many grey squares did she need if the most outer layer had 9 squares on each side?
- How many squares are there in the Figure 19?
(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 19
= [(19 x 2) - 1]
2 = 37 x 37
= 1369
Answer(s): (a) 49; (b) 1369