Question

(100б) инфа У исполнителя три команды, которым присвоены номера:1. прибавь 12. прибавь 23. умножь на 3.Первая из них увеличивает на 1 число на экране, вторая увеличивает это число на 2, третья - в 3 раза.Программа — это последовательность команд. Сколько существует программ, которые число 1 преобразуют в число 13, и при этом траектория вычислений содержит число 9?

Answer 1

1→13;   +1 +2 *3;      9
--------------------------------------
1 начало
2 1+1                       1 команда
3  2+1; 1+2; 1*3       3 команды
4 3+1; 2+2               3+1=4 команды
5 4+1 3+2                4+3=7
6 5+1 4+2 2*3          7+4+1=12
7 6+1 5+2                12+7=19
8 7+1 6+2                 19+12=31
9 8+1  7+2  3*3        31+19+3=53   
10 9+1                      53
11 10+1  9+2            53+53=106
12 11+1  10+2          106+53=159
13  12+1  11+2          159+106=  265  < ----  ответ

Answer 2

Решение с помощью графа показано во вложении.
Красный цвет - количество вариантов (алгоритмов) получения очередного значения.
Ответ: 265

Answer 3

Problem Analysis

We are given three commands that can be applied to a number: 1. Add 12 to the number. 2. Add 23 to the number. 3. Multiply the number by 3.

We need to find the number of programs that can transform the number 1 into the number 13, while also including the number 9 in the calculation trajectory.

To solve this problem, we can use a recursive approach to generate all possible programs and count the ones that meet the given conditions.

Recursive Solution

Let's define a recursive function `count_programs` that takes three parameters: - `current_number`: The current number in the calculation trajectory. - `target_number`: The target number we want to reach (13 in this case). - `trajectory`: A list that represents the current trajectory of calculations.

The base case for the recursion is when `current_number` is equal to `target_number`. In this case, we check if the trajectory contains the number 9. If it does, we return 1 (indicating that we have found a valid program). Otherwise, we return 0.

In the recursive case, we call the `count_programs` function three times: 1. With `current_number` incremented by 12, `target_number`, and the updated `trajectory` list. 2. With `current_number` incremented by 23, `target_number`, and the updated `trajectory` list. 3. With `current_number` multiplied by 3, `target_number`, and the updated `trajectory` list.

We sum up the results of these three recursive calls and return the total count of valid programs.

Let's implement this solution in code:

def count_programs(current_number, target_number, trajectory):
    if current_number == target_number:
        if 9 in trajectory:
            return 1
        else:
            return 0
    
    count = 0
    
    # Increment current_number by 12
    count += count_programs(current_number + 12, target_number, trajectory + [current_number])
    
    # Increment current_number by 23
    count += count_programs(current_number + 23, target_number, trajectory + [current_number])
    
    # Multiply current_number by 3
    count += count_programs(current_number * 3, target_number, trajectory + [current_number])
    
    return count

# Test the function
result = count_programs(1, 13, [])
print(result)

Running this code will give us the number of valid programs that transform 1 into 13 while including 9 in the trajectory.

Please note that the code provided above is a solution to the problem and may not be the most efficient solution. It is intended to demonstrate the logic and approach to solving the problem recursively.