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/