Here's a way:
Invite user "butlerbot" to your board. It will automatically create a "Butler" list in your board.
In the "Butler" list, add a card with the following title:
every day at 6pm, count the cards in list "X"
Every day, the bot will automatically post a comment on that same card with the number of cards in the list. If your timezone is not U.S. Eastern, you also need to add another card with a title such as:
my timezone is Europe/London
A list of all the timezones supported by the bot can be found here: Timezones
There's a ton of other stuff the bot can do, check it out here: Butler Bot for Trello. You can also contact the author and request support in that same board. Disclosure: I'm the author.