Olympiad problems

May Olympiad L1 - geometry, 2019.4

You have to divide a square paper into three parts, by two straight cuts, so that by locating these parts properly, without gaps or overlaps, an obtuse triangle is formed. Indicate how to cut the square and how to assemble the triangle with the three parts.

2022 Kyiv City MO Round 1, Problem 5

Tags: cutting the paper , combinatorics

Find the smallest integer $n$ for which it's possible to cut a square into $2n$ squares of two sizes: $n$ squares of one size, and $n$ squares of another size. [i](Proposed by Bogdan Rublov)[/i]

2019 May Olympiad, 4

Tags: combinatorics , geometry , cutting the paper , paper , obtuse triangle , square

You have to divide a square paper into three parts, by two straight cuts, so that by locating these parts properly, without gaps or overlaps, an obtuse triangle is formed. Indicate how to cut the square and how to assemble the triangle with the three parts.

2015 Sharygin Geometry Olympiad, 4

Tags: geometry , convex quadrilateral , partition , cutting the paper

Prove that an arbitrary convex quadrilateral can be divided into five polygons having symmetry axes. (N. Belukhov)