Question

на загадочном калькуляторе есть Волшебная кнопка при нажатии которой к числу на экране прибовляется его сумма цифр .Сначала на экране было число 52 ,а затем много раз нижимали волшебную кнопку.Могло ли при этом в какой-то момент на экране появиться число 3663?

Answer 1

The Mysterious Calculator

The Mysterious Calculator has a Magical Button that, when pressed, adds the sum of the digits of the number on the screen to the number itself. The initial number on the screen was 52, and the Magical Button was pressed multiple times. The question is whether, at some point, the number 3663 could appear on the screen.

To determine if the number 3663 could appear on the screen, let's analyze the process step by step.

1. Starting with the number 52: - The sum of the digits of 52 is 5 + 2 = 7. - Adding the sum of the digits to 52 gives us 52 + 7 = 59.

2. Pressing the Magical Button again: - The sum of the digits of 59 is 5 + 9 = 14. - Adding the sum of the digits to 59 gives us 59 + 14 = 73.

3. Pressing the Magical Button once more: - The sum of the digits of 73 is 7 + 3 = 10. - Adding the sum of the digits to 73 gives us 73 + 10 = 83.

4. Continuing this process: - Pressing the Magical Button repeatedly will continue to add the sum of the digits to the current number on the screen.

Based on this analysis, it is not possible for the number 3663 to appear on the screen. The sum of the digits of 52 is 7, and adding 7 repeatedly will never result in a number with a sum of digits equal to 6 + 6 + 3 = 15.

Therefore, it is not possible for the number 3663 to appear on the screen of the Mysterious Calculator.

[[1]]