The figure shows a pattern formed using some toothpicks.
- How many toothpicks are used to form 56 squares?
- How many squares can be formed using 445 toothpicks?
(a)
Pattern for the number of toothpicks
1 square: 1 x 3 + 1 = 4
2 squares: 2 x 3 + 1 = 7
3 squares: 3 x 3 + 1 = 10
Formula
Number of toothpicks = Number of squares x 3 + 1
Number of toothpicks for 56 squares
= 56 x 3 + 1
= 169
(b)
Number of squares x 3 + 1 = 445
Number of squares x 3 = 445 - 1
Number of squares = 444 ÷ 3
Number of squares = 148
Answer(s): (a) 169; (b) 148