6 square tile in a 11x11 square table
Source: Czech-Polish-Slovak Junior Match 2016, team p4 CPSJ
January 20, 2020
Tilingcombinatoricscombinatorial geometry
Problem Statement
Several tiles congruent to the one shown in the picture below are to be fit inside a square table, with each tile covering whole unit squares, no sticking out the square and no overlapping.
(a) Determine the greatest number of tiles which can be placed this way.
(b) Find, with a proof, all unit squares which have to be covered in any tiling with the maximal number of tiles.
https://cdn.artofproblemsolving.com/attachments/c/d/23d93e9d05eab94925fc54006fe05123f0dba9.png
Poland