Three views of a stack of sugar cubes are shown below. What is the MINIMUM number of cubes that are required to produce this stack?
Show Hint
To minimize cubes, always match the largest column height with the largest row height at their intersection. This dual-satisfaction technique reduces the count of high columns dramatically.
Step 1: Honour all three views. Place cubes only where the top, front and side silhouettes all demand one. Step 2: Count the minimum. Layer-by-layer this minimal stack needs 25 cubes. \[ \boxed{25} \]