MySQL - Is it possible to assign permission to count the number of tables in a database without permissions on individual tables?
One option would be to give the user access to a single non-NULL column that doesn't provide very much information, but will allow COUNT(*) to succeed.

For example:

GRANT SELECT(TABLE_TYPE) ON INFORMATION_SCHEMA.TABLES TO blind_user@localhost;

Now, blind_user@localhost can execute SELECT COUNT(*) FROM INFORMATION_SCHEMA.TABLES but can't get any private data out of the table itself.