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2022 AMC 10B Problem 3

Problem 3 of 25EasierNumber TheoryCounting & Probability

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

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Solution

There are 910=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 905=450.90\cdot5=450. Thus, the answer is D .

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Concepts: digits · parity · multiplication principle

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.