Problems

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.

Daniel has drawn on a sheet of paper a circle and a dot inside it. Show that he can cut a circle into two parts which can be used to make a circle in which the marked point would be the center.

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

Is it possible to cut such a hole in \(10\times 10 \,\,cm^2\) piece of paper, though which you can step?

A square \(4 \times 4\) is called magic if all the numbers from 1 to 16 can be written into its cells in such a way that the sums of numbers in columns, rows and two diagonals are equal to each other. Sixth-grader Edwin began to make a magic square and written the number 1 in certain cell. His younger brother Theo decided to help him and put the numbers \(2\) and \(3\) in the cells adjacent to the number \(1\). Is it possible for Edwin to finish the magic square after such help?

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