Math Problem Statement
How many whole numbers between 1 and 100 use the digit "6" at least once?
Solution
To find the number of whole numbers between 1 and 100 that use the digit "6" at least once, we can follow these steps:
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Total numbers between 1 and 100: There are 100 numbers from 1 to 100 inclusive.
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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 .
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Counting the number "100": The number "100" does not contain the digit "6".
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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" = .
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:
- How many whole numbers between 1 and 1000 use the digit "6" at least once?
- How many whole numbers between 1 and 200 use the digit "7" at least once?
- How would the count change if considering numbers without leading zeros?
- How many whole numbers between 1 and 500 use at least one of the digits "3" or "6"?
- 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!
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Number Theory
Formulas
Total Numbers = 100
Count of numbers without '6'
Theorems
Complementary Counting
Suitable Grade Level
Grades 6-8
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