How many whole numbers between 1 and 100 use the digit "6" at least once?

To find the number of whole numbers between 1 and 100 that use the digit "6" at least once, we can follow these steps:

1. **Total numbers between 1 and 100:** There are 100 numbers from 1 to 100 inclusive.

2. **Numbers without the digit "6":**
   - For a one-digit number, it can be any of 1-9 except 6, which leaves 8 options (1, 2, 3, 4, 5, 7, 8, 9).
   - For two-digit numbers, both digits must not be "6":
     - The first digit (tens place) can be 1-9 except 6, so 8 choices (1, 2, 3, 4, 5, 7, 8, 9).
     - The second digit (ones place) can be 0-9 except 6, so 9 choices (0, 1, 2, 3, 4, 5, 7, 8, 9).
   - Thus, the total count of two-digit numbers without "6" is \(8 \times 9 = 72\).

3. **Counting the number "100":** The number "100" does not contain the digit "6".

4. **Calculating numbers with at least one "6":**
   - Numbers without "6" are 8 (one-digit) + 72 (two-digit) = 80.
   - So, the numbers containing at least one "6" = \(100 - 80 = 20\).

Thus, there are **20 whole numbers between 1 and 100 that use the digit "6" at least once**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How many whole numbers between 1 and 1000 use the digit "6" at least once?
2. How many whole numbers between 1 and 200 use the digit "7" at least once?
3. How would the count change if considering numbers without leading zeros?
4. How many whole numbers between 1 and 500 use at least one of the digits "3" or "6"?
5. What is the probability that a randomly selected number between 1 and 100 contains the digit "6"?

**Tip:** When dealing with digits in numbers, systematically consider each place value (units, tens, hundreds, etc.) for accurate counting!

How many whole numbers between 1 and 100 use the digit '6' at least once?

Discover how to calculate the number of whole numbers between 1 and 100 that contain the digit '6' at least once. This problem introduces combinatorics and complementary counting, making it ideal for students in Grades 6-8.

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