Question 15
Alex builds seven towers from equal-sized wooden cubes, as shown.
To make their heights equal, Alex may add or remove cubes. Adding one cube or removing one cube counts as one move. For example, changing the leftmost tower to height 2 needs at least 3 moves (remove 3 cubes), while changing it to height 7 needs at least 2 moves (add 2). Moving a cube from one tower to another counts as two moves. What is the smallest number of moves needed to make all seven towers equally tall?
To make their heights equal, Alex may add or remove cubes. Adding one cube or removing one cube counts as one move. For example, changing the leftmost tower to height 2 needs at least 3 moves (remove 3 cubes), while changing it to height 7 needs at least 2 moves (add 2). Moving a cube from one tower to another counts as two moves. What is the smallest number of moves needed to make all seven towers equally tall?