Many hours wasted on this pursuit. Let me save you time. When you change to permalinks, if your .htaccess file is not writable, copy and paste the code they give you. (if you can’t save the file, open it with sudo and enter your password).
Open up Terminal and browse to: /private/etc/apache2/users
Inside that directory you should a file with your username and ‘.conf’ at the end (example: jdoe.conf). Open that file and make it look like this (obviously replace ‘/Users/username/Sites‘ with your username ‘/Users/jdoe/Sites‘)
Options Indexes MultiViews
Allow from all
Restart Apache and permalinks should now work.
Note: I am not using MAMP (as it is outdated with regards to the PHP version) and I have updated the PHP that comes installed on Macs. I am also using the Apache2 files that come baked in your Mac. I also have this working with a virtual host so that is cool too. I recommend you try to set this up if you are not a newbie.