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 62?
- How many sticks are needed to make structure 178?
- A structure is made using 268 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 62
= 62 x 8 + 4
= 500
(b)
Number of sticks for structure 178
= 178 x 8 + 4
= 1428
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 268 sticks
= (268 - 4) ÷ 8
= 264 ÷ 8
= 33
Answer(s): (a) 500; (b) 1428; (c) 33