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cuting 2 regular polygons, folding one piece from each to create another

Source: Sharygin 2010 Final 8.7

October 2, 2018
geometryregular polygonpaperPolygons

Problem Statement

Each of two regular polygons PP and QQ was divided by a line into two parts. One part of PP was attached to one part of QQ along the dividing line so that the resulting polygon was regular and not congruent to PP or QQ. How many sides can it have?