Question

Исполнитель Чертёжник пе¬ре¬ме¬ща¬ет¬ся на ко¬ор¬ди¬нат¬ной плоскости, остав¬ляя след в виде линии. Чертёжник может вы¬пол¬нять ко¬ман¬ду Сместиться на (a, b) (где a, b — целые числа), пе¬ре¬ме¬ща¬ю¬щую Чертёжника из точки с координатами (x, у) в точку с ко¬ор¬ди¬на¬та¬ми (x + а, у + b). Если числа a, b положительные, зна¬че¬ние со¬от¬вет¬ству¬ю¬щей ко¬ор¬ди¬на¬ты увеличивается; если отрицательные, уменьшается. Например, если Чертёжник на¬хо¬дит¬ся в точке с координатами (4, 2), то ко¬ман¬да Сме¬стить¬ся на (2, −3) пе¬ре¬ме¬стит Чертёжника в точку (6, −1). Запись Повтори k раз Команда1 Команда2 Ко¬ман¬даЗ Конец означает, что по¬сле¬до¬ва¬тель¬ность ко¬манд Команда1 Команда2 КомандаЗ по¬вто¬рит¬ся k раз. Чертёжнику был дан для ис¬пол¬не¬ния сле¬ду¬ю¬щий алгоритм: Повтори 4 paз Сместиться на (−1, −1) Сме¬стить¬ся на (2, 2) Сме¬стить¬ся на (3, −3) Конец Какую ко¬ман¬ду надо вы¬пол¬нить Чертёжнику, чтобы вер¬нуть¬ся в ис¬ход¬ную точку, из ко¬то¬рой он начал движение? 1) Сместиться на (−16, −8) 2) Сместиться на (16, 8) 3) Сместиться на (16, −8) 4) Сместиться на (−16, 8)

Answer 1

Ответ: 4.
Упрощаем алгоритм: Смещение на (-1, -1) и потом на (2, 2) = смещение (1, 1). Упрощаем дальше, (1, 1) + (3, -3) = (4, -2)
Умножаем (4, -2) на 4 повтора и получаем (16, -8).
Тк он двигается в обратную сторону, инвертируем, получаем (-16, 8)
Готово. Ответ: 4

Answer 2

Understanding the Problem

The problem describes a scenario where a draftsman is moving on a coordinate plane, leaving a trace in the form of a line. The draftsman can execute a command called "Move to" that takes two integers, (a, b), as parameters. This command moves the draftsman from a point with coordinates (x, y) to a point with coordinates (x + a, y + b). If the values of a and b are positive, the corresponding coordinate increases; if they are negative, the coordinate decreases.

The problem also provides an algorithm that the draftsman needs to execute. The algorithm consists of a sequence of commands that need to be repeated a certain number of times. The goal is to determine which command the draftsman needs to execute in order to return to the starting point.

Analyzing the Algorithm

The given algorithm is as follows:

Repeat 4 times
    Move to (-1, -1)
    Move to (2, 2)
    Move to (3, -3)
End

To determine the command that will return the draftsman to the starting point, we need to analyze the effect of each command on the draftsman's position.

1. The command "Move to (-1, -1)" will move the draftsman from the current position (x, y) to the position (x - 1, y - 1). 2. The command "Move to (2, 2)" will move the draftsman from the current position (x, y) to the position (x + 2, y + 2). 3. The command "Move to (3, -3)" will move the draftsman from the current position (x, y) to the position (x + 3, y - 3).

Calculating the Final Position

To calculate the final position of the draftsman after executing the algorithm, we need to apply each command in the sequence and keep track of the changes in the coordinates.

Starting with the initial position (x, y) = (0, 0), we can calculate the final position as follows:

1. After the first iteration: - Move to (-1, -1): (x, y) = (0 - 1, 0 - 1) = (-1, -1)

2. After the second iteration: - Move to (2, 2): (x, y) = (-1 + 2, -1 + 2) = (1, 1)

3. After the third iteration: - Move to (3, -3): (x, y) = (1 + 3, 1 - 3) = (4, -2)

4. After the fourth iteration: - Move to (-1, -1): (x, y) = (4 - 1, -2 - 1) = (3, -3)

Therefore, the final position of the draftsman after executing the algorithm is (x, y) = (3, -3).

Determining the Command to Return to the Starting Point

To determine the command that will return the draftsman to the starting point, we need to calculate the reverse of each command in the sequence.

1. The reverse of the command "Move to (-1, -1)" is "Move to (1, 1)". 2. The reverse of the command "Move to (2, 2)" is "Move to (-2, -2)". 3. The reverse of the command "Move to (3, -3)" is "Move to (-3, 3)".

Therefore, the draftsman needs to execute the command "Move to (-3, 3)" in order to return to the starting point.

Answer

The command that the draftsman needs to execute in order to return to the starting point is "Move to (-3, 3)" (option 4).

Please let me know if you need any further assistance!