Question

На доске записано число 61. Каждую минуту число стирают с доски и записывают на это место произведение его цифр, увеличенное на 13. То есть, через одну минуту на доске будет записано 19 (6 умножить на 1+13= 19). Какое число можно будет прочитать на доске через 1 час?Помогите пожалуйста!!!Срочно, буду очень благодарна)))Заранее спасибо))

Answer 1

Короче)
2ая минута 9*1+13=22
3ая минута 2*2+13=17
4ая минута 7*1+13= 20
5ая минута 2*0+13=13
6ая минута 1*3+13= 16
7ая минута 1*6+13=19
и так они будут повторяться, ну и если посчитать то через час будет на доске цифра 19

Answer 2

Problem Analysis

We are given that the number 61 is written on a board. Every minute, the number is erased and replaced with the product of its digits, increased by 13. We need to determine the number that will be written on the board after 1 hour.

Solution

To solve this problem, we can simulate the process of erasing and replacing the number on the board for 60 minutes.

Starting with the number 61, we calculate the product of its digits, which is 6 * 1 = 6. We then add 13 to this product, resulting in 19. This becomes the new number on the board after 1 minute.

For the next minute, we repeat the process with the number 19. The product of its digits is 1 * 9 = 9, and adding 13 gives us 22. This becomes the new number on the board after 2 minutes.

We continue this process for 60 minutes, updating the number on the board each time. Finally, after 60 minutes, we will have the number that will be written on the board.

Let's calculate the number that will be written on the board after 1 hour:

1. Start with the number 61. 2. Calculate the product of its digits: 6 * 1 = 6. 3. Add 13 to the product: 6 + 13 = 19. 4. Repeat steps 2 and 3 for 59 more times.

Calculation

Let's calculate the number that will be written on the board after 1 hour:

Starting number: 61

Minute 1: 6 * 1 + 13 = 19

Minute 2: 1 * 9 + 13 = 22

Minute 3: 2 * 2 + 13 = 17

Minute 4: 1 * 7 + 13 = 20

Minute 5: 2 * 0 + 13 = 13

Minute 6: 1 * 3 + 13 = 16

Minute 7: 1 * 6 + 13 = 19

Minute 8: 1 * 9 + 13 = 22

Minute 9: 2 * 2 + 13 = 17

Minute 10: 1 * 7 + 13 = 20

...

Minute 59: 2 * 0 + 13 = 13

Minute 60: 1 * 3 + 13 = 16

After 1 hour (60 minutes), the number written on the board will be 16.

Conclusion

After simulating the process of erasing and replacing the number on the board for 60 minutes, we determined that the number that will be written on the board after 1 hour is 16.