The following is a sequence of structures made by joining identical cubes with 1-cm sticks as edges.
- How many sticks are needed to make structure 50?
- How many sticks are needed to make structure 206?
- A structure is made using 420 sticks. Which structure is it?
(a)
Pattern for the number of sticks
Structure 1: 1 x 8 + 4= 12
Structure 2: 2 x 8 + 4 = 20
Structure 3: 3 x 8 + 4 = 28
Formula
Number of sticks = Structure number x 8 + 4
Number of sticks for structure 50
= 50 x 8 + 4
= 404
(b)
Number of sticks for structure 206
= 206 x 8 + 4
= 1652
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 420 sticks
= (420 - 4) ÷ 8
= 416 ÷ 8
= 52
Answer(s): (a) 404; (b) 1652; (c) 52