An oblong is a rectangle whose width and length are consecutive integers: 1x2, 2x3, 3x4, etc. Does N exist such that it is possible to split the first N oblongs into 2 or more non-intersecting sets so that the oblongs in any of these sets tile a square?
$\begingroup$
$\endgroup$
4
asked Oct 31, 2018 at 2:03
-
1$\begingroup$ It seems that searching the first 25 oblongs tiling squares with sidelength 60 and 40 may be promising. $\endgroup$– LeechLatticeCommented Oct 31, 2018 at 3:22
-
$\begingroup$ Do you have any examples of oblongs tiling a square, Bernardo? $\endgroup$– Gerry MyersonCommented Oct 31, 2018 at 12:51
-
$\begingroup$ A converse problem of tiling oblongs with squares was posed at math.stackexchange.com/questions/2057290/… $\endgroup$– Gerry MyersonCommented Oct 31, 2018 at 12:57
-
2$\begingroup$ Yes, @GerryMyerson: Tiles 2x3, 3x4, 4x5, 5x6, 6x7, 7x8, and 9x10 tile a square of side 16. I think they are pretty common. $\endgroup$– Bernardo Recamán SantosCommented Oct 31, 2018 at 13:07
Add a comment
|