Open math problems which high school students can understand I request people to list some moderately and/or very famous open problems which high school students,perhaps with enough contest math background, can understand, classified by categories as on arxiv.org. Please include statement of the theorems,if possible, and if there are specific terms, please state what they mean.
Thank you.I am quite inquisitive to know about them and I asked this question after seeing how Andrew J.Wiles was fascinated by Fermat's last theorem back in high school.

Chromatic Number of the Plane (Hadwiger-Nelson Problem): What is the minimum number of colors required to color the plane so that no two points which are unit distance apart are the same color? The current bounds on $\chi$ (which is commonly used to denote this number) are 
$$4\leq \chi \leq 7.$$
The book The Mathematical Coloring Book by Alexander Soifer focuses primarily around this problem, giving a thorough history of the problem and it's creators and presenting the current state of the problem and some of it's generalizations. 
