The figure shows a pattern formed using some toothpicks.
- How many toothpicks are used to form 59 squares?
- How many squares can be formed using 211 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 59 squares
= 59 x 3 + 1
= 178
(b)
Number of squares x 3 + 1 = 211
Number of squares x 3 = 211 - 1
Number of squares = 210 ÷ 3
Number of squares = 70
Answer(s): (a) 178; (b) 70