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 61?
- How many sticks are needed to make structure 195?
- A structure is made using 204 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 61
= 61 x 8 + 4
= 492
(b)
Number of sticks for structure 195
= 195 x 8 + 4
= 1564
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 204 sticks
= (204 - 4) ÷ 8
= 200 ÷ 8
= 25
Answer(s): (a) 492; (b) 1564; (c) 25