Question

О. Могут ли в однокруговом турнире пятнадцати шахматистов какие-то четыре участника набрать в сумме больше очков, чем все остальные вместе? Если да, то приведите пример турнира, иначе объясните почему нет. За победу даётся 1 очко, за ничью 0,5 очка, за проигрыш 0 очков. Помогите пожалуйста ​

Answer 1

Ответ:Да

Пошаговое объяснение:Нужно что бы каждый из этих четырёх шахматистов выграли у всех, а у других друга сыграли ничьи, тогда они наберут в сумме 46,а оставшиеся 11 шахматистов смогут набрать лишь 10 баллов в сумме

Answer 2

Can four participants in a round-robin tournament of fifteen chess players accumulate more points than all the others combined?

In a round-robin tournament, each participant plays against every other participant exactly once. In this case, we have a round-robin tournament with fifteen chess players. The scoring system awards 1 point for a win, 0.5 points for a draw, and 0 points for a loss.

To determine if it is possible for four participants to accumulate more points than all the others combined, we need to consider the maximum number of points that can be earned in the tournament.

In a round-robin tournament with n participants, the maximum number of points that can be earned is given by the formula:

Maximum Points = (n-1) * (n/2) For a round-robin tournament with fifteen participants, the maximum number of points that can be earned is:

Maximum Points = (15-1) * (15/2) = 14 * 7 = 98 points

Now, let's consider the scenario where four participants accumulate more points than all the others combined. In this case, the four participants would need to earn a total of 99 or more points, while the remaining eleven participants would need to earn a total of less than 99 points.

However, this scenario is not possible because the maximum number of points that can be earned in the tournament is 98 points. Therefore, it is not possible for four participants to accumulate more points than all the others combined in a round-robin tournament with fifteen chess players.

To summarize, it is not possible for four participants in a round-robin tournament of fifteen chess players to accumulate more points than all the others combined because the maximum number of points that can be earned in the tournament is 98 points, which is less than the required total of 99 points.

I hope this explanation clarifies the situation. Let me know if you have any further questions!