1. INTRODUCTION. We say that a set S of 2n + 1 points in the plane is in general position if no three of the points are collinear and no four are concyclic. We call a circle halving with respect to S if it has three points of S on its circumference, n − 1 points in its interior, and n − 1 in its exterior. The goal of this paper is to prove the following surprising fact: any set of 2n + 1 points...

A study was carried out among 76 students who took part in the Olympiad contests practical medical skills an innovative distance format. The data obtained testify to effectiveness of simulation training, assessment which by answering test questions before and after passing task, as well assessing students' actions during remote passage scenario experts.

Recently, a backgammon bot named Palamedes won the first prize in backgammon at the 16 Computer Olympiad. Palamedes is an ongoing work aimed at developing intelligent bots to play a variety of popular backgammon variants. Currently, the Greek variants Portes, Plakoto and Fevga are supported. A different neural network has been designed, trained and evaluated for each one of these variants. This...

Each year a wealth of informatics olympiads are held worldwide at national, regional and international levels, all of which require engaging and challenging tasks that have not been seen before. Nevertheless, creating high quality tasks can be a difficult and time-consuming process. In this paper we explore some of the different techniques that problem setters can use to find new ideas for task...

Geometry is not only a part of mathematics with ancient roots but also a vivid area of modern research. Especially the field of geometry, called by some negligence “elementary”, continues to attract the attention also of the great community of leisure mathematicians. This is probably due to the small set of prerequisites necessary to formulate the problems posed in this area and the erudition a...

In recent years the Monte Carlo tree search revolution has spread from computer Go to many areas, including computer Hex. MCTS Hex players now outperform traditional knowledge-based alpha-beta search players, and the reigning Computer Olympiad Hex gold medallist is the MCTS player MoHex. In this paper we show how to strengthen MoHex, and observe that — as in computer Go — using learned patterns...

Geometry is not only a part of mathematics with ancient roots but also a vivid area of modern research. Especially the field of geometry called by some negligence “elementary” continues to attract the attention also of the great community of leisure mathematicians. This is probably due to the small set of prerequisites necessary to formulate the problems posed in this area and the erudition and...