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MathNet 2019-part-07 — 184 problems (EN–VI) Question 71

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 71

Bogdan drew $2017$ vertical and $2018$ horizontal lines in the rectangle $Q$. These lines divide $Q$ into $2018 \times 2019$ smaller not necessarily equal rectangles. Two children want to determine the perimeter of $Q$. Andrew says that he can do it by choosing some $2019$ smaller rectangles and getting to know their perimeters. On the contrary, Olesya says that she can do it by choosing $4036$ smaller rectangles. Who is right about the number of smaller rectangles, perimeters of which one should know in order to determine the perimeter of $Q$?

(Bogdan Rublyov)