3.7.234. Smallest square for packing consecutive dominoes

Find the smallest square S where one can place n rectangles of respective size 1Γ—2,2Γ—4,β‹―,nΓ—2Β·n so that they do not overlap and so that their borders are parallel to the borders of S. Each rectangle can be rotated by 90 degrees. The problem is described in http://www.stetson.edu/~efriedma/domino/. FigureΒ 3.7.65 gives a solution for n=22 found by H.Β Simonis.

Figure 3.7.65. A solution to the smallest square for packing consecutive dominoes problem for n=22