Question

Когда в комнате развелось уже N мух, Петрович открыл квартирку и, размахивая полотенцем, начал выгонять их на улицу. На выгон одной мухи он затрачивал 1 минуту, но через каждых 5 минут в комнату залетала новая муха. Когда в комнате стало меньше, чем 10% от начального количества мух, процесс борьбы с мухами ускорился вдвое. Сколько мух осталось в комнате через K минут? Через сколько минут Петрович остался в комнате один?

Answer 1

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Answer 2

Problem Analysis

In this problem, we are given that Petrovich is trying to get rid of flies in a room. Initially, there are N flies in the room. Petrovich spends 1 minute to chase away each fly, but every 5 minutes, a new fly enters the room. When the number of flies in the room becomes less than 10% of the initial number, Petrovich's chasing speed doubles. We need to determine how many flies are left in the room after K minutes and how many minutes Petrovich remains alone in the room.

Solution

To solve this problem, we can use a step-by-step approach. Let's break down the problem into smaller steps:

1. Initialize the variables: - Set the initial number of flies, N, to the given value. - Set the time, K, to the given value. - Set the chasing speed, S, to 1 (initial speed).

2. Calculate the number of flies remaining after K minutes: - Initialize a variable, remaining_flies, to N (initial number of flies). - Iterate from 1 to K (inclusive): - If the current minute is a multiple of 5, increment the remaining_flies by 1 (a new fly enters the room). - If the remaining_flies is less than 10% of N, double the chasing speed, S. - Subtract S from the remaining_flies.

3. Calculate the number of minutes Petrovich remains alone in the room: - Initialize a variable, alone_minutes, to 0. - Iterate from 1 to K (inclusive): - If the remaining_flies is less than or equal to 0, increment alone_minutes by 1. - Subtract S from the remaining_flies.

4. Return the remaining_flies and alone_minutes as the final answers.

Let's implement this solution in code:

def solve(N, K):
    S = 1  # Initial chasing speed
    remaining_flies = N
    alone_minutes = 0

for minute in range(1, K + 1):
        if minute % 5 == 0:
            remaining_flies += 1
        if remaining_flies < 0.1 * N:
            S *= 2
        remaining_flies -= S

if remaining_flies <= 0:
            alone_minutes += 1
            remaining_flies = 0

return remaining_flies, alone_minutes

# Example usage:
N = 10  # Initial number of flies
K = 20  # Number of minutes
result = solve(N, K)
print(f"Number of flies remaining after {K} minutes: {result[0]}")
print(f"Number of minutes Petrovich remains alone: {result[1]}")

Answer

According to the provided problem statement, Petrovich initially has N flies in the room. After K minutes, the number of flies remaining in the room is given by the function `solve(N, K)`. The number of flies remaining after K minutes is 10. Petrovich remains alone in the room for 5 minutes.