Mathematical Games and Strategies. Method of Filling Up to a Fixed Number

Abstract

Mathematical game-based problems are one of the types of text-based mathematical problems, the solution of which
requires a fairly high level of logical thinking and requires observation and precise, concise reasoning from the solver. Problems
that contain mathematical games are often found at mathematical olympiads for students of different levels. We will consider
text-based problems containing such search and olympiad mathematical games. To solve such problems, first of all, if possible,
a winning strategy for the game should be formed. Therefore, our discussions will often concern who will win in the case of the
correct game, we will figure out what the correct strategy of a mathematical game is and how to play to win. We will consider
such mathematical games with a winning strategy, the solution of which will use the method of winning positions. Games and
strategies are a separate class of mathematical problems. Most often, two people play in such problems, the rules of the game are
determined by the condition of the problem. It is necessary to show which player has the opportunity to win regardless of the
opponent's moves. The article discusses specific problems, for the solution of which the method of filling up to a fixed number
is used, and also the inverse problems of the problems considered. In particular, we have given that for some numbers there is a
winning strategy of a mathematical game and it is necessary to determine the specific values of these numbers, sometimes the
interval in which this number can be placed. Such problems belong to the category of very difficult problems. Appropriate
methodological conclusions have been made.