Question 15
Alex the beaver has equal-sized wooden cubes. He uses them to build seven towers, as shown below.
To make all towers the same height, Alex can add cubes or remove cubes already in the towers. Adding or removing one cube counts as one move. For example, changing the leftmost tower's height to 2 takes at least 3 moves, by removing 3 cubes. Changing its height to 7 takes at least 2 moves, by adding 2 cubes. Moving a cube from one tower to another counts as 2 moves.
What is the fewest moves Alex needs to make all the towers the same height?
To make all towers the same height, Alex can add cubes or remove cubes already in the towers. Adding or removing one cube counts as one move. For example, changing the leftmost tower's height to 2 takes at least 3 moves, by removing 3 cubes. Changing its height to 7 takes at least 2 moves, by adding 2 cubes. Moving a cube from one tower to another counts as 2 moves.
What is the fewest moves Alex needs to make all the towers the same height?