Cube pile
Rick has five cubes, each one 2cm taller than the previous one. The largest is the same height as a tower built of the two smallest. How high would a tower of all five cubes be?
Age
11 to 14
Challenge level
Problem
Rick has five cubes. Each one is 2cm taller than the previous one.
The largest cube is the same height as a tower built of the two smallest cubes.
How high would a tower of all five cubes be?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 50 cm
Smallest cube: $h$ cm
Other cubes: $h+2$, $h+4$, $h+6$ and $h+8$ cm
Largest as tall as two smallest: $h+\underbrace{h+2}_8=h+8\\
h+2=8\\
h=6$
Height of tower: $6+8+10+12+14 = 20 + 20 + 10 = 50$ cm