Problem

Source: Iran 3rd round 2011-combinatorics exam-p6

Tags: combinatorics proposed, combinatorics



Every bacterium has a horizontal body with natural length and some nonnegative number of vertical feet, each with nonnegative (!) natural length, that lie below its body. In how many ways can these bacteria fill an $m\times n$ table such that no two of them overlap? proposed by Mahyar Sefidgaran