Olympiad problems

2022 Kyiv City MO Round 1, Problem 5

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]

combinatorics cutting the paper

2015 Sharygin Geometry Olympiad, 4

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

geometry convex quadrilateral partition cutting the paper partitions

2019 May Olympiad, 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.

obtuse triangle paper geometry combinatorics square cutting the paper

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.

obtuse triangle paper geometry combinatorics square cutting the paper