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stingin two squares connected by a curve

Source: Mongolian MO 2002 Teachers P6

April 9, 2021
geometrygame

Problem Statement

Two squares of area 3838 are given. Each of the squares is divided into 3838 connected pieces of unit area by simple curves. Then the two squares are patched together. Show that one can sting the patched squares with 3838 needles so that every piece of each square is stung exactly once.