Combinatorics · Combinatorial game · Parity · Invariant · Winning strategy
Lara and Sara draw \(n\) straight lines on a rectangular sheet of paper, taking turns and drawing one line each time. Every line is parallel to one of the edges of the sheet and runs from edge to edge, and no line may lie along an edge or on top of a line already drawn. At the end the sheet is cut into a number of rectangles. Lara wins if that number is odd, Sara wins if it is even.
Depending on \(n\) and on which of them draws first, determine who has a winning strategy.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2012, 1. letnik, category A, problem B3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source