Problems

Among 4 people there are no three with the same name, the same middle name and the same surname, but any two people have either the same first name, middle name or surname. Can this be so?

Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?

Snow White cut out a big square of cotton fabric and placed it in a chest. The first gnome came, took out the square of fabric from the chest, cut it into four squares, put these back in the chest and left. Later the second gnome came and took out one of the squares and then cut it into four pieces and placed all of these in the chest. Then came the third gnome. He also took out one of the squares and cut it into four squares and put them all back in the chest. The rest of the gnomes also did the same thing. How many squares of fabric were in the chest after the seventh gnome left?

Cut the following shape into two equal parts.

Cut the following figure into two equal parts.

Cut the following shape into four equal figures.

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

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

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

Cut a square into two equal:
1. Triangles.
2. Pentagons
3. Hexagons.