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OPM 2009 Problem 3

  • Final day 1

Duarte wants to draw a square whose side's length is 20092009 cm and which is divided in 2009×20092009\times2009 squares whose side's length is 11 cm and whose sides are parallel to the original square's one, without taking the pencil out of the paper. Starting on one of the vertex of the giant square, what is the length of the shortest line that allows him to make this drawing?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Portuguese Mathematical Olympiad 2009 official paper, page 1.

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