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 51?
- How many sticks are needed to make structure 199?
- A structure is made using 404 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 51
= 51 x 8 + 4
= 412
(b)
Number of sticks for structure 199
= 199 x 8 + 4
= 1596
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 404 sticks
= (404 - 4) ÷ 8
= 400 ÷ 8
= 50
Answer(s): (a) 412; (b) 1596; (c) 50