Problems

Cut the following figure into two equal parts.

Find all rectangles that can be cut into \(13\) equal squares.

Cut a square into \(3\) parts which you can use to construct a triangle with angles less than \(90^{\circ}\) and three different sides.

Does there exist a quadrilateral which can be cut into six parts with two straight lines?

Cut the following shape into four equal figures.

Cut the following shape into two equal parts.

Find one way to encrypt letters of Latin alphabet as sequences of \(0\)s and \(1\)s, each letter corresponds to a sequence of five symbols.

Using the representation of Latin alphabet as sequences of \(0\)s and \(1\)s five symbols long, encrypt your first and last name.

Decipher the quote from "Alice in Wonderland" from the following matrix:
\[\begin{array}{@{}*{26}{c}@{}} Y&q&o&l&u&e&c&d&a&i&n \\ w&a&r&l&a&w&e&a&t&y&k \\ s&n&t&c&a&e&k&c&e&a&m \\ t&o&d&r&w&e&a&t&a&h&r \\ a&c&n&t&n&e&o&d&t&r&h \\ n&i&d&n&l&g&m&e&x&s&z \end{array}\]

Decipher the following quote from Alice in Wonderland:
Lw zrxog eh vr qlfh li vrphwklqj pdgh vhqvh iru d fkdqjh.
The same letters correspond to the same in the phrase, different letters correspond to different. We know that no original letters stayed in place, meaning that in places of e,r,h there was surely something else.