Thus, the minimum number is $1$, since the full hall can be covered by a single valid rectangle.

Sun, 03 May 2026 16:06:20 +0000

Discover Why the Minimum Ground Coverage Number in Hall Design Is $1 When planning optimal space usage—such as in event halls, auditoriums, or public venues—designers often ask: What is the smallest meaningful unit of coverage? The answer lies comfortably at $1, meaning a single valid rectangle can fully cover any rectangular hall. This concept, rooted deeply in geometry and spatial efficiency, reveals why $1$ represents the absolute minimum number of rectangles required. ### The Mathematics Behind Efficient Hall Coverage In geometric terms, a rectangular hall can be perfectly represented—and covered—by a single rectangle: itself. Unlike more fragmented arrangements involving multiple partial rectangles, using one full valid shape eliminates overlaps, gaps, and wasted space. This results in maximum coverage efficiency with zero redundancy. Therefore, no smaller number of rectangles than $1$ can achieve full hall coverage, establishing $1$ as the definitive baseline.