# Problems

The problems for the International Tournament are suggested by contemporary mathematicians and satisfy the following criteria:

each problem is

*partially unsolved*, i.e. it may contain parts with no known solution,each problem is

*accessible to high school students*, i.e. the authors are certain that some elementary research work can be done on the problem.

The original problems come from the fields of algebra, analysis, combinatorics, geometry and number theory.

Here is the **official list of problems** for the ITYM 2019:

Problems 2019 (PDF)

**Updates:**

**Apr 19** • In the problem 8, the definition of an embedding has changed (the condition that no arc includes points associated with other vertices was also removed).

**Apr 17** • In the problem 8, the definition of an embedding has changed (the condition of non-intersection of arcs was removed).

**Mar 26** • In the problem 3 question 1(b), the variables *a* and *b* have been discarded.

**Mar 26** • In the problem 8 question 2, the definition of a perfect *k*-ary tree has changed.

**Remark 1.** Please also check for possible updates of the list of problems during the next days after they are published.

**Remark 2,** The questions are not always ranked by increasing order of difficulty. Besides, there is no need to give solutions to all the problems: each team can refuse a certain number of problems. Refer to the regulation for details.

If you have questions or remarks please write to oc@itym.org

** Archives**

** **ITYM 2018: Problems 2018 — Quiz 2018

ITYM 2017: Problems 2017 — Quiz 2017

ITYM 2016: Problems 2016 — Quiz 2016

ITYM 2015: Problems 2015 — Quiz 2015 / Solution (Quiz)

ITYM 2014: Problems 2014

ITYM 2013: Problems 2013

ITYM 2012: Problems 2012

ITYM 2011: Problems 2011

ITYM 2010: Problems 2010

ITYM 2009: Problems 2009

**Authors**