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This article concerns the mathematical problem of finding the maximum retention of water on various surfaces. Imagine a surface of cells of various heights on a regular array such as a square lattice, and water is rained down on every cell in the system. The boundaries of the system are open and allow water to flow out. Water will be trapped in ponds, and eventually all ponds will fill to their maximum height, with any additional water flowing over spillways and out the boundaries of the system. The problem is to find the amount of water trapped or retained for a given surface.

This has been studied extensively for two mathematical surfaces: (1) Magic Square and (2) Random Surfaces (discussed in this entry). In 2010, water retention on magic squares was used as a challenge in Al Zimmermann contest: find the L x L magic square with the maximum water retention. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Water retention on mathematical surfaces". This entry is a fragment of a larger work. Link may die if entry is finally removed or merged.