Question

За несколько часов до начала футбольного матча у пяти касс стадиона, которые пока закрыты, собирается очередь. Сейчас у первой кассы стоят 6 человек, у второй — 7, у третьей — 8, у четвертой — 9 и у пятой — 10. Каждую минуту к кассам подходят 8 человек, и каждый встаёт в произвольную очередь. В какой-то момент оказалось, что во всех очередях одинаковое число человек. Определите наименьшее возможное такое число.

Answer 1

Через пять минут
Надо взять число которое кратно и пяти и восьми.

Answer 2

Problem Analysis

We are given that there are five closed ticket counters at a stadium, and a queue has formed a few hours before the start of a football match. Currently, there are 6 people at the first counter, 7 people at the second counter, 8 people at the third counter, 9 people at the fourth counter, and 10 people at the fifth counter. Every minute, 8 people join the queues at random counters. We need to determine the minimum possible number of people in each queue when it is observed that all queues have the same number of people.

Solution

To find the minimum possible number of people in each queue when all queues have the same number of people, we need to find the least common multiple (LCM) of the current number of people in each queue.

The LCM of two numbers can be found by dividing their product by their greatest common divisor (GCD). We can extend this approach to find the LCM of multiple numbers.

Let's calculate the LCM of the current number of people in each queue.

1. Calculate the product of the current number of people in each queue: 6 * 7 * 8 * 9 * 10 = 30,240. 2. Calculate the GCD of the current number of people in each queue. We can use the Euclidean algorithm to find the GCD. - GCD(6, 7) = 1 - GCD(1, 8) = 1 - GCD(1, 9) = 1 - GCD(1, 10) = 1 - The GCD of all the numbers is 1. 3. Calculate the LCM using the formula: LCM = (product of numbers) / (GCD of numbers) = 30,240 / 1 = 30,240.

Therefore, the minimum possible number of people in each queue when all queues have the same number of people is 30,240.

Answer

The minimum possible number of people in each queue when all queues have the same number of people is 30,240.