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2022 AMC 10B Problem 3

Problem 3 of 25EasierNumber TheoryCombinatorics

How many three-digit positive integers have an odd number of even digits?

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Solution

There are 9⋅10=909\cdot10=90 choices for the hundreds and tens digits. Once those two digits are fixed, the units digit must have whichever parity makes the total number of even digits odd. There are always 55 digits of the required parity (including 00 among the even digits). Therefore, the number of integers is 90⋅5=450.90\cdot5=450. Thus, the answer is D .
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Tagged: digits · parity · multiplication principle

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