If n ≥ 3, then any sequence of squares of side lengths not greater than 1 whose total area does not exceed ¼(n+1) can be on-line packed into n unit squares.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-2-5, author = {Janusz Januszewski}, title = {On-line Packing Squares into n Unit Squares}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {58}, year = {2010}, pages = {137-145}, zbl = {1215.52007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-2-5} }
Janusz Januszewski. On-line Packing Squares into n Unit Squares. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) pp. 137-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-2-5/