what is the maximal number of consecutive 3-digit numbers that have at least one odd digit?

To find the maximum number of consecutive 3-digit numbers that have at least one odd digit, we can begin by identifying the first and last numbers in the sequence.

First, we need to determine the first 3-digit number with at least one odd digit. Since the digits in a 3-digit number range from 0 to 9, there are five odd digits: 1, 3, 5, 7, and 9. However, the first digit of a 3-digit number cannot be 0, so we can exclude it.

The smallest possible first digit is 1, and the largest possible first digit is 9. Any odd digit can occupy the second and third positions. Therefore, the first 3-digit number with at least one odd digit is 101.

Next, we need to identify the last 3-digit number with at least one odd digit. Since we want consecutive numbers, the last number would be the largest 3-digit number that has at least one odd digit. This number is 999.

Now, we can calculate the maximum number of consecutive 3-digit numbers with at least one odd digit by subtracting the first number from the last number and adding 1: 999 - 101 + 1 = 899.

Therefore, the maximal number of consecutive 3-digit numbers that have at least one odd digit is 899.