Question

Рыцарский турнир длится ровно 7 дней.к концу четвертого дня сэр Ланселот не успел сразиться лишь с одной четвертью от общего числа участников турнира.А сэр Тристан к этому времени сразился ровно с одной седьмой из тех рыцарей с кем успел сразиться сэр Ланселот.Какое минимальное количество рыцарей могло учавствовать в турнире?

Answer 1

Минимальное количество рыцарей семь

Answer 2

Finding the Minimum Number of Knights in the Tournament

To find the minimum number of knights that could have participated in the tournament, we can use the information provided about Sir Lancelot and Sir Tristran's progress in the tournament.

Given: - The tournament lasts for 7 days. - By the end of the fourth day, Sir Lancelot had only fought a quarter of the total number of participants. - By the end of the fourth day, Sir Tristran had fought exactly one-seventh of the knights Sir Lancelot had fought.

Calculating the Minimum Number of Knights

Let's denote the total number of knights in the tournament as N.

1. By the end of the fourth day, Sir Lancelot had fought a quarter of the total number of participants: - This means Sir Lancelot fought N/4 knights by the end of the fourth day.

2. By the end of the fourth day, Sir Tristran had fought exactly one-seventh of the knights Sir Lancelot had fought: - This means Sir Tristran fought N/28 knights by the end of the fourth day.

To find the minimum number of knights, we need to find a value for N that satisfies both conditions.

Solving for the Minimum Number of Knights

We need to find the minimum value of N such that Sir Lancelot fought a quarter of the total number of participants and Sir Tristran fought exactly one-seventh of the knights Sir Lancelot had fought.

Let's solve for N: - Sir Lancelot fought N/4 knights by the end of the fourth day. - Sir Tristran fought N/28 knights by the end of the fourth day.

To satisfy both conditions, the minimum number of knights N can be calculated as: N = LCM(4, 28), where LCM is the Least Common Multiple of 4 and 28.

Calculating the Least Common Multiple (LCM)

The LCM of 4 and 28 can be calculated as follows: - LCM(4, 28) = (4 * 28) / GCD(4, 28), where GCD is the Greatest Common Divisor of 4 and 28.

Calculating the Greatest Common Divisor (GCD)

The GCD of 4 and 28 is 4.

Final Calculation

Using the GCD, the LCM of 4 and 28 is: LCM(4, 28) = (4 * 28) / 4 = 28

Therefore, the minimum number of knights that could have participated in the tournament is 28.

Conclusion: The minimum number of knights that could have participated in the tournament is 28.