How to delete contacts from iPhone?

I just set up my brand new iPhone 5 running iOS 6. I set it up as a new device. I have been using Exchange to sync my contacts with Google (Gmail) Contacts for the past few days. Today I stopped doing that and started syncing via CardDAV.

However I have some contacts that I can't delete. In fact, if I turn off all contact syncing (including iCloud) I am still left with 50 contacts that I can't delete. I try to delete them, but they just stay there.

Any thoughts on how to solve this?

Update: Note that I have tried a restore (and restored from backup) on the iPhone and this did not fix it.

Solution 1:

Just go to your contact via contacts app icon. Select desired contact then click edit in top right corner and then scroll down to very bottom and click delete contact, voilá!