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2007 JBMO TST- Macedonia, problem 5

Source: 2007 JBMO TST- Macedonia

May 28, 2019
JuniorJMMOMacedonia2007geometrycombinatorics

Problem Statement

We are given an arbitrary △ABC\bigtriangleup ABC. a) Can we dissect △ABC\bigtriangleup ABC in 44 pieces, from which we can make two triangle similar to △ABC\bigtriangleup ABC (each piece can be used only once)? Justify your answer! b) Is it possible that for every positive integer n≥2n \ge 2 , we are able to dissect △ABC\bigtriangleup ABC in 2n2n pieces, from which we can make two triangles similar to △ABC\bigtriangleup ABC (each piece can be used only once)? Justify your answer!
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