Question 22
A digit game is played where a student writes down each positive integer from 1 to n consecutively which forms a big number. Then, in each turn, the student will remove some digit(s) found in the middle according to this rule:
- If the number of digits in the array is odd, then the student must delete one digit in the middle.
- If the number of digits in the array is even, then the student must delete two digits in the middle.
This process is repeated until the student gets the smallest possible multiple of 9. For example, Nala writes the numbers from 1 to 15 as follows: 123456789101112131415. In the first turn, she decides to delete 0 and the result is 12345678911112131415. In the second turn, she deletes 1 and 1 and so on, until she gets the smallest multiple of 9, which is 1215, after 9 turns.
If she writes the number from 1 to 2022, what is the minimum possible number of times will she do this process in order to get the smallest possible multiple of 9?
- If the number of digits in the array is odd, then the student must delete one digit in the middle.
- If the number of digits in the array is even, then the student must delete two digits in the middle.
This process is repeated until the student gets the smallest possible multiple of 9. For example, Nala writes the numbers from 1 to 15 as follows: 123456789101112131415. In the first turn, she decides to delete 0 and the result is 12345678911112131415. In the second turn, she deletes 1 and 1 and so on, until she gets the smallest multiple of 9, which is 1215, after 9 turns.
If she writes the number from 1 to 2022, what is the minimum possible number of times will she do this process in order to get the smallest possible multiple of 9?