ISL 2007 C2
A unit square is dissected into rectangles such that their sides are parallel to the sides of the square. Any line, parallel to a side of the square and intersecting its interior, also intersects the interior of some rectangle. Prove that in this dissection, there exists a rectangle having no point on the boundary of the square. (Japan)
Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.
Official text: IMO 2007 Shortlist booklet, page 29.
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).