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?
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Start with the $16$ cubes forced by the complete top view. Then overlap equal front-view and side-view peak requirements at common grid cells so that each extra vertical cube serves both silhouettes.
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. \[ \boxed{25} \]