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min no of regular triangles to cover the lines of a diagram

Source: (2021-) 2022 XV Dürer Math Competition Finals Day2 E4

December 1, 2022
combinatoricsisosceles

Problem Statement

At least how many regular triangles are needed to cover the lines of the following diagram? https://cdn.artofproblemsolving.com/attachments/e/3/4de2ed2c7cc9421d7d060f0bc537ccaa3838fc.png (Only the perimeter of the triangles is involved in the covering, and the entire perimeter need not be incident on the diagram.)