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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_7 / A digital display shows the current date as an 8-digit integer consisting of a 4-digit year, followed by a 2-digit month, followed by a 2-digit date within the month. For example, …

Problem

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problem

A digital display shows the current date as an

8

-digit integer consisting of a

4

-digit year, followed by a

2

-digit month, followed by a

2

-digit date within the month. For example, Arbor Day this year is displayed as 20230428. For how many dates in

2023

will each digit appear an even number of times in the 8-digital display for that date?

Plain-text mathematical notation (without MathML)

A digital display shows the current date as an 8-digit integer consisting of a 4-digit year, followed by a 2-digit month, followed by a 2-digit date within the month. For example, Arbor Day this year is displayed as 20230428. For how many dates in 2023 will each digit appear an even number of times in the 8-digital display for that date?

Original LaTeX notation

A digital display shows the current date as an $8$-digit integer consisting of a $4$-digit year, followed by a $2$-digit month, followed by a $2$-digit date within the month. For example, Arbor Day this year is displayed as 20230428. For how many dates in $2023$ will each digit appear an even number of times in the 8-digital display for that date?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_7
task_id: de693fc8-b378-59a9-95e1-0050749e184a
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f7
task_revision_id: 2
config / split: default / train

Official source

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