Question

22. В автобус помещается не более 20 пассажиров. Пустой автобус подъехал к первой остановке, где в него вошёл один человек. На каждой последующей остановке в автобус входило вдвое больше людей, чем на предыдущей. Начиная с третьей остановки, из автобуса начали выходить по 2 человека на каждой остановке. На пятой остановке автобус ожидало вдвое больше людей, чем на четвёртой, но всем не хватило мест. Сколько человек не поместилось в автобус на пятой остановке? В ответе пиши только число

Answer 1

1) 1
2) 1 + 2
3) 1 + 2 + 4 - 2
4) 1 + 2 + 4 + 8 - 4
5) 1 + 2 - 2 + 4 - 2 + 8 - 2 + 16
Ответ: 5 людям не хватило места

Answer 2

Problem Analysis

We are given the following information: - The bus can accommodate a maximum of 20 passengers. - The bus starts empty and one person boards at the first stop. - At each subsequent stop, the number of people boarding is twice the number of people who boarded at the previous stop. - Starting from the third stop, two people exit the bus at each stop. - At the fifth stop, there are twice as many people waiting to board as there were at the fourth stop, but there is not enough space for everyone.

We need to determine how many people could not fit on the bus at the fifth stop.

Solution

To solve this problem, we can simulate the process of people boarding and exiting the bus at each stop.

Let's start by keeping track of the number of people on the bus at each stop. We'll initialize a variable `passengers` to 0 to represent the number of people on the bus initially.

At each stop, we'll update the number of passengers based on the given conditions: - At the first stop, one person boards the bus, so we'll add 1 to `passengers`. - At each subsequent stop, the number of people boarding is twice the number of people who boarded at the previous stop. We'll multiply the number of people who boarded at the previous stop by 2 and add it to `passengers`. - Starting from the third stop, two people exit the bus at each stop. We'll subtract 2 from `passengers` at each stop.

We'll continue this process until the fifth stop and then check if there is enough space on the bus for the people waiting to board at the fifth stop. If there is not enough space, we'll calculate the number of people who could not fit on the bus.

Let's calculate the number of people who could not fit on the bus at the fifth stop.

Solution Steps

1. Initialize the variable `passengers` to 0. 2. At the first stop, add 1 to `passengers`. 3. At each subsequent stop (from the second to the fifth stop), do the following: - Multiply the number of people who boarded at the previous stop by 2 and add it to `passengers`. - Subtract 2 from `passengers` to account for the people exiting the bus. 4. Check if there is enough space on the bus for the people waiting to board at the fifth stop: - If the number of people waiting to board at the fifth stop is greater than the remaining capacity on the bus (20 - `passengers`), calculate the number of people who could not fit on the bus. - If there is enough space, the number of people who could not fit on the bus is 0. 5. Return the number of people who could not fit on the bus at the fifth stop.

Let's calculate the number of people who could not fit on the bus at the fifth stop.

Solution

Based on the given information, we can calculate the number of people who could not fit on the bus at the fifth stop.

1. Initialize the variable `passengers` to 0. 2. At the first stop, add 1 to `passengers`. `passengers = 1`. 3. At the second stop, multiply the number of people who boarded at the previous stop (1) by 2 and add it to `passengers`. `passengers = 1 + 2 = 3`. 4. At the third stop, multiply the number of people who boarded at the previous stop (2) by 2 and add it to `passengers`. `passengers = 3 + 4 = 7`. 5. At the fourth stop, multiply the number of people who boarded at the previous stop (4) by 2 and add it to `passengers`. `passengers = 7 + 8 = 15`. 6. At the fifth stop, there are twice as many people waiting to board as there were at the fourth stop. However, there is not enough space on the bus for everyone. The remaining capacity on the bus is 20 - 15 = 5. Since there are more than 5 people waiting to board, we can calculate the number of people who could not fit on the bus. The number of people who could not fit on the bus is the difference between the number of people waiting to board and the remaining capacity on the bus. The number of people waiting to board is twice the number of people who boarded at the fourth stop, which is 2 * 8 = 16. Therefore, the number of people who could not fit on the bus is 16 - 5 = 11.

Answer: 11