Problem 15 · 2022 Math Kangaroo
Hard
Counting & Probability
careful-countingplace-value
How many integers between 100 and 300 have only odd digits?
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Answer: A — 25
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Hint 1 of 2
'Only odd digits' means every digit is 1,3,5,7 or 9; think about what the hundreds digit can be between 100 and 300.
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Hint 2 of 2
Count independent choices for hundreds, tens and units digits and multiply.
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Approach: count digit choices and multiply
- Between 100 and 300 the hundreds digit must be odd, so it can only be 1 (200s have an even hundreds digit).
- The tens and units digits each have 5 odd choices.
- That gives 1 x 5 x 5 = 25 numbers, so the answer is A.
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