Why do this problem?
is an appealing context in which to explore numbers. It could be used at the start of a new year to draw attention to the new calendar.
Have you got a system of working so that you don't miss any dates out?
How are you recording the dates you've found?
What years are likely to give you palindromic dates?
The problem Today's Date
would make a good follow-up task.
Encouraging children to concentrate on a year at a time will make this challenge more accessible.