Start of the qual­i­fy­ing round

The par­ti­cipants are sup­posed to be school stu­dents of grades equi­val­ent to Rus­si­an grades 5–11 (11–17 years old). Those from coun­tries with a dif­fer­ent sys­tem of grades will be able to choose their sets of prob­lems accord­ing to the table of match­ing grades (for some coun­tries) or accord­ing to the age of stu­dents: Rus­si­an Grade 5 cor­res­ponds approx­im­ately to 2005 year of birth, grade 11 — to 1999.

Here is the first (cor­res­pond­ence) round of competition.

Please remem­ber that your solu­tion of every prob­lem should include full reas­on­ing, and not only the right answer.

We will be happy if your friends who like math­em­at­ics also par­ti­cip­ate. How­ever, every work should be done per­son­ally; oth­er­wise, your paper will not be considered.

Please be care­ful with mak­ing up of your work, fol­low the rules and declare all neces­sary data. You need not include state­ments of prob­lems into your paper; please write down your solu­tions only.

It appeared that the organ­izers do not have a solu­tion of one of the prob­lems in the grade R11. In any case, we are going to score sig­ni­fic­ant advances towards the solu­tion, and we can­not exclude that someone will ulti­mately find a solution.

You can write your solu­tions by hand and scan them or type them using a text edit­or. Solu­tions should be writ­ten in Esper­anto, Bul­gari­an, Eng­lish, French, Ger­man, Geor­gi­an, Hebrew, Per­sian, Romani­an, Rus­si­an, Span­ish, Ukrain­i­an, or Uzbek; use of oth­er lan­guages should be agreed with the organ­izers in advance. For anonym­ous grad­ing, you should not write down your name on the paper sheets with solutions.

Before sub­mit­ting your solu­tions, please fill in a ques­tion­naire. (Please down­load it in Excel format if MS Excel is avail­able. Oth­er­wise, please copy the ques­tions from the second page and add your answers in an .odt or a .txt file.)

The solu­tions should be sub­mit­ted to the Jury before Novem­ber 18.

Please indic­ate your grade of par­ti­cip­a­tion (R5, …, R11) in the Sub­ject line.