Packing problems: Difference between revisions

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People are given {{mvar|n}} [[unit square]]s and have to pack them into the smallest possible container, where the container type varies:
 
* [[Square packing in a square|Packing squares in a '''square''']]: Optimal solutions have been proven for {{mvar|n}} from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any [[square number|square]] [[integer]]. The wasted space is asymptotically {{math|[[Big O notation|O]](''a''{{sup|73/115}})}}.
* [[Square packing in a circle|Packing squares in a '''circle''']]: Good solutions are known for {{math|''n'' ≤ 35}}.[[Image:10 kvadratoj en kvadrato.svg|thumb|120px|right|The optimal packing of 10 squares in a square]]