2023 AMC 10A Problems/Problem 9
A digital display shows the current date as an 
-digit integer consisting of a 
-digit year, followed by a 
-digit month, followed by a -digit date within the month. For example, Arbor Day this year is displayed as 20230428. For how many dates in 
will each digit appear an even number of times in the 8-digital display for that date?
Solution
Do careful casework by each month. In the month and the date, we need a 
, a 
, and two digits repeated. After the case work, we get 
, meaning the answer 
For those who are wondering, the numbers are:
20230113, 20230131, 20230223, 20230311, 20230322, 20231013, 20231031, 20231103, 20231130.
