Question

Игра с фишками. Фишек неограниченное количество.Стол симметричный относительно центра.На стол по очереди два игрока укладывают фишки до тех пор, пока есть свободное место. Выигрывает игрок последним положивший фишку.ВОПРОС Какой игрок выигрывает, делающий первый или второй ход?Разработать 100% выигрышный алгоритм – тактику игры.

Answer 1

Если стол симметричный, то скорее всего на него поместится равное кол-во фишек(с той и с другой стороны), а значит число четное. В конце игры получиться, что последнее свободное место займет  фишка второго игрока и первому игру некуда будет ложить свои фишки. Ну значит нужно ходить вторым игроком )

Answer 2

Introduction

In this game with an unlimited number of chips and a symmetrical table, two players take turns placing chips on the table until there is no more space. The player who places the last chip wins. The question is, which player, the one who makes the first move or the one who makes the second move, has a winning strategy?

Analysis

To determine the winning strategy, let's consider the possible scenarios and analyze the outcomes for each player.

1. If there is only one chip left on the table, the player who makes the first move will win by placing the last chip. 2. If there are two chips left on the table, the player who makes the first move will lose. No matter where they place their chip, the second player can mirror their move and place the last chip. 3. If there are three chips left on the table, the player who makes the first move can guarantee a win. They can place their chip in the center, forcing the second player to mirror their move. The first player can then place their second chip anywhere, leaving the second player with no valid move. 4. If there are four chips left on the table, the player who makes the first move will lose. No matter where they place their chip, the second player can mirror their move and place the last chip.

Based on this analysis, we can see that the winning strategy depends on the number of chips left on the table. If the number of chips is divisible by four, the second player will win. Otherwise, the first player will win.

Conclusion

In conclusion, the player who makes the first move will win if the number of chips left on the table is not divisible by four. Otherwise, the second player will win. This analysis provides a 100% winning algorithm for the game.