Question

Трое друзей — Дима, Володя и Боря — играют в бадминтон. После каждой партии победитель продолжает игру в следующей партии с третьим участником. Когда они закончили, оказалось, что Дима сыграл 17 партий, а Володя — 23. Какое наименьшее количество партий мог сыграть Боря? а) 13 б) 14 в) 23 г) 17

Answer 1

Ответ: 17, это точно, можешь не сомневаться.

Answer 2

Problem Analysis

Three friends, Dima, Volodya, and Borya, are playing badminton. After each game, the winner continues playing in the next game with the third participant. Dima played 17 games, and Volodya played 23 games. We need to determine the minimum number of games Borya could have played.

Solution

To find the minimum number of games Borya could have played, we need to consider the total number of games played by Dima and Volodya.

Let's assume Borya played x games. Since each game has one winner, the total number of games played by Dima, Volodya, and Borya would be:

Dima's games + Volodya's games + Borya's games = Total games

Substituting the given values:

17 + 23 + x = Total games

Simplifying the equation:

40 + x = Total games

Since we want to find the minimum number of games Borya could have played, we need to find the smallest possible value for x.

Looking at the answer choices, we can see that the options are 13, 14, 23, and 17. Let's evaluate each option:

a) 13: If Borya played 13 games, the total number of games would be 40 + 13 = 53. This is not a valid option since it is greater than the total number of games played by Dima and Volodya.

b) 14: If Borya played 14 games, the total number of games would be 40 + 14 = 54. This is not a valid option since it is greater than the total number of games played by Dima and Volodya.

c) 23: If Borya played 23 games, the total number of games would be 40 + 23 = 63. This is not a valid option since it is greater than the total number of games played by Dima and Volodya.

g) 17: If Borya played 17 games, the total number of games would be 40 + 17 = 57. This is a valid option since it is equal to the total number of games played by Dima and Volodya.

Therefore, the minimum number of games Borya could have played is 17.

Answer

The minimum number of games Borya could have played is 17.