PSLE
Cody wanted to build a set of steps with 3-cm cubes. The figures show how he built the steps from a height of 6 cm to 9 cm to 12 cm. If Cody continued building the steps in this way, what would be the height of the set of steps that had 156 cubes? Express your answer in cm.
Cubes needed for 6-cm steps = 2 x 3 = 2 x (1 + 2) = 6 cubes
Cubes needed for 9-cm steps = 2 x 6 = 2 x (1 + 2 + 3) = 12 cubes
Cubes needed for 12-cm steps = 2 x 10 = 2 x (1 + 2 + 3 + 4) = 20 cubes

Formula:
Number of cubes needed for the set of steps
= 2 x (1 + 2 + 3 + ... + Height)
= 2 x ^{(Height) x (Height + 1)}₂ 
= Height x (Height + 1)

Height x (Height + 1) = 156
12 x 13 = 156

Number of cubes needed for the height of the set of steps that had 156 cubes = 12 

Height of the set of steps that had 156 cubes
= 12 x 3 
= 36 cm

Answer(s): 36 cm