A stack of cubes stands on a 3 by 3 grid. From the front it looks like the left drawing, and from the right-hand side like the right drawing. What is the least number of cubes the stack can contain?

Work layer by layer. Bottom layer: the front view needs 3 columns and the side view 3 rows, and 3 cubes placed on a diagonal cover both: 3. Second layer: 2 columns and 2 rows are needed: 2 cubes. Third layer: 1 column and 1 row: 1 cube. Least total $3+2+1=6$. (14 is the most the stack could hold.)