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#### Dissections with certain properties

Is it possible to cut a square into four parts so that each part touches each of the other three $($ie has common parts of a border$)$?

#### Dissections with certain properties , Unusual constructions

Is it possible to cut out such a hole in a sheet of paper through which a person could climb through?

#### Dissections with certain properties , Examples and counterexamples. Constructive proofs , Simple fractions

A rectangle is cut into several smaller rectangles, the perimeter of each of which is an integer number of meters. Is it true that the perimeter of the original rectangle is also an integer number of meters?

#### Dissections with certain properties , Tables and tournaments (other)

Cut the board shown in the figure into four identical parts so that each of them contains three shaded cells.

#### Dissections with certain properties

Cutting into four parts. Cut each of the figures into four equal parts $($you can cut along the sides and diagonals of cells$)$.

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