Question

На доске написано число. Ребёнок играет в арифметическую игру: он может либо стереть последнюю цифру написанного числа, либо прибавить к написанному числу число 2018 и записать полученный результат, стерев предыдущее число. Может ли ребёнок, действуя таким образом, в конце концов получить число 1? Какое наименьшее пятизначное число может получиться, если на доске записано число 42?

Answer 1

Ответ:

Получить 1 невозможно потому что если прибавить четное число к четному получится четное.

10132

Пошаговое объяснение:

42+2018=2060

2060+2018=4078

4078+2018=6096

6096+2018=8114

8114+2018=10132

Answer 2

Problem Analysis

A child is playing an arithmetic game where they can either erase the last digit of a given number or add 2018 to the number and erase the previous number. The goal is to determine if the child can eventually reach the number 1 by following these rules. We are given that the initial number on the board is 42 and we need to find the smallest five-digit number that can be obtained using this game.

Solution

To solve this problem, we need to analyze the possible outcomes of the game and determine if the number 1 can be reached. Let's start with the initial number 42 and see what happens when we apply the game rules.

1. Erase the last digit: The number becomes 4. 2. Add 2018: The number becomes 2022. 3. Erase the last digit: The number becomes 202. 4. Add 2018: The number becomes 2220. 5. Erase the last digit: The number becomes 222. 6. Add 2018: The number becomes 2240. 7. Erase the last digit: The number becomes 224. 8. Add 2018: The number becomes 2242. 9. Erase the last digit: The number becomes 224.

At this point, we can see that the number 1 cannot be reached by applying the game rules to the initial number 42. The number keeps repeating the sequence 4 -> 2022 -> 2220 -> 2240 -> 2242 -> 224. Therefore, it is not possible to reach the number 1.

Now, let's find the smallest five-digit number that can be obtained using this game. We can start with the initial number 42 and apply the game rules until we reach a five-digit number.

1. Erase the last digit: The number becomes 4. 2. Add 2018: The number becomes 2022. 3. Erase the last digit: The number becomes 202. 4. Add 2018: The number becomes 2220. 5. Erase the last digit: The number becomes 222. 6. Add 2018: The number becomes 2240. 7. Erase the last digit: The number becomes 224. 8. Add 2018: The number becomes 2242. 9. Erase the last digit: The number becomes 224.

The smallest five-digit number that can be obtained using this game is 224.

Answer: The child cannot reach the number 1 by following the game rules. The smallest five-digit number that can be obtained using the initial number 42 is 224.