Courses for teachers of Mathematics on a regular basis began to be held on September 15, 2019, at the Institute of Mathematics of the National Academy of Sciences of Ukraine with the support of Borys Grinchenko Kyiv University and the Institute of Postgraduate Education.

Physics Club for the 7-8 grade students began to work from April 1, 2019, at the Faculty of Physics of the Taras Shevchenko National University of Kyiv in the framework of the project of Minor Academic University with the support of Kyiv Academic University and the Mathematics Club "Quantum".

A girl named Varia from Odessa, who is in the second grade and is very interested in Mathematics has contacted us, asking for interesting math problems, which she could solve at home alone or with her parents. We try to fulfill this request of Varia and select a consistent cycle of interesting math problems so that she can further train her abilities of logical thinking. This course may be useful for other children who are interested in Mathematics. Therefore, we decided to place such problems on our website. Other boys and girls may be interested in solving them and sending us their solutions.

For convenience, we have created a form, via which you can submit your solutions. We will answer only those solutions that will be justified. The work must be scanned and sent using this form in a single **pdf**-file. You can use, for example, the service **pdfjoiner.com**. The file name must start with your last name. It is desirable to use black or dark blue paste for registration of work so that the text you will write could be legible.

To upload images, right-click and select “save image”.

Lesson 5. Problems on the chessboard

Mathematics can be mastered by anyone who is interested in it. However, sometimes the interest comes later, or there is no opportunity at school to find interesting tasks. At the same time, mathematical knowledge is arranged in such a way that each subsequent level is based on the previous one. In order to give everyone the opportunity to try to master different mathematical techniques and ways of thinking, we decided to systematize mathematical knowledge in such a way as to help form an integral mathematical perspective from elementary school to the PhD examination. This system of knowledge will be filled consistently. We hope that our work will be useful and bring pleasure to all who want to learn to think critically.