Problem

Source: Rioplatense Olympiad 2011 level 3 P5

Tags: combinatorial geometry, rectangle, combinatorics



A form is the union of squared rectangles whose bases are consecutive unitary segments in a horizontal line that leaves all the rectangles on the same side, and whose heights $m_1, ... , m_n$ satisying $m_1\ge ... \ge m_n$. An angle in a form consists of a box $v$ and of all the boxes to the right of $v$ and all the boxes above $v$. The size of a form of an angle is the number of boxes it contains. Find the maximum number of angles of size $11$ in a form of size $400$. source