Problems

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.

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?

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

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?

Welcome back! We hope you all had a great summer and now you are ready for the new school year full of fun problems in mathematics. We decided to start with warm-up topic called dissections, so today we will cut various shapes into more elaborate geometric figures in order to reassemble them into a different shape.

Cut the following shape into four equal figures.

Cut the following shape into two equal parts.

Today we will practice to encrypt and decipher information using some of the most common codes. Majority of the codes in use can be alphabetic and numeric, namely one may want to encode a word, a phrase, or a number, or just any string of symbols using either letters, or numbers, or both. Some of the codes, however may use various other symbols to encrypt the information. To solve some of the problems you will need the correspondence between alphabet letters and numbers

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