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Problem A. 663. (February 2016)

A. 663. There are given two positive integers: \(\displaystyle k\) and \(\displaystyle \ell\). A square with horizontal and vertical sides is divided into finitely many rectangles by line segments such that the following statements are satisfied: \(\displaystyle (i)\) every horizontal or vertical line of the plane contains at most one of the segments; \(\displaystyle (ii)\) no two segments cross each other in their interiors; \(\displaystyle (iii)\) every horizontal line, intersecting the square but not containing any of the segments, intersects exactly \(\displaystyle k\) rectangles; \(\displaystyle (iv)\) every vertical line, intersecting the square but not containing any of the segments, intersects exactly \(\displaystyle \ell\) rectangles. What can be the number of rectangles?

Russian problem

(5 pont)

Deadline expired on 10 March 2016.


Statistics:

8 students sent a solution.
5 points:Baran Zsuzsanna, Gáspár Attila, Glasznova Maja, Imolay András, Williams Kada.
1 point:1 student.
0 point:2 students.

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