Hi,
I've just purchased an iPad and couldn't remember my security questions for my AppleID account, therefor was unable to reset my security questions (I know right). I have found a solution to this and wanted to share it.
This will only apply to those that:
Had an old account and didn't enable 2-factor authentication
Did not have a recovery phone number setup
Are unable to reset security questions on the iForgot website or log into appleid.apple.com.
Contacted Apple support and didn't get anywhere
All you need to do is get a iPad / iPhone, do a factory reset on it then during the initial setup you select the option to restore from iCloud. At this point it will ask for a mobile number (Doesn't have to be an iPhone number) and it will enable 2-factor authentication. It told me that I didn't have any data in iCloud and returned me to the previous screen where I setup the device as new.
Note: I did this on an old iPhone, my iPad told me to enter a verification code that it sent to the iPhone, but for some reason I had to click 'did not get anything' and enter my phone number where it send my phone a text and I was able to authenticate it.
Finally... I was able to log into appleid.apple.com and view my account.
I hope this helps at lease one person, there were plenty of people online who had this issue:
https://www.reddit.com/r/apple/comments/6obk1b/the_struggles_with_apple_id_security_questions/ (This post provides an alternate resolution that didn't for for me and is possibly 'patched' by Apple)
https://www.reddit.com/r/apple/comments/6xz0hn/is_there_no_way_to_reset_your_apple_security/
https://www.reddit.com/r/apple/comments/6016dc/question_i_forgot_my_security_questions_answers/
https://www.reddit.com/r/applehelp/comments/1lqfia/forgot_appleid_security_questions/
TLDR: Select the 'Restore from iCloud' on the initial welcome screens.Edit: After logging into my AppleID account, I was unable to access the security questions - I assume this has been replaced with the 2FA option.
If you can't remember your answers ...
Have a look at: If you forgot the answers to your Apple ID security questions
At Apple ID, follow the onscreen steps to verify your identity. If you don't get any options to verify your identity, you can't reset your security questions at this time.
Choose new security questions and answers and select Continue.
If you need more help, contact Apple Support
If you log in with your Apple ID on a device (any iOS 10+/macOS 10.12+ device should work), log out and do that several times, you'll eventually get a popup to enable 2FA... and it will let you do that without answering a single security question! I got the popup after logging in and out just once, but your results may vary.
Note: if you have macOS, you can use this method without logging out from your main account on your device - just create a new user, log in, and you'll be asked to link your iCloud account. (thanks for the tip, kallax!)
Others have confirmed that this method still works:
I had a very old Apple ID with remaining credit that was only used for iTunes and not yet activated for iCloud. I had already changed the password via the email address some time ago. But resetting the security questions was not possible anymore, because I could not answer enough questions for that. And after several attempts even this form was blocked for the meantime.
On an old iPhone 4s (iOS 9.3.6) the Apple ID was still stored under iTunes & App Store (I don't know if it is required to use a device which was already linked to this Apple ID). I also entered the same Apple ID under iCloud to activate iCloud for this Apple ID. I then entered my phone number under iCloud > Apple ID > Contact information (confirmed by code from SMS). Entering an additional email adress was at this stage not possible. Thereafter, under iCloud > Apple ID > Password & Security, the two-factor authentication could be enabled for the same phone number (eventually an unlock code has to be set prior under Settings). I had to confirm the activation via the code sent by SMS. Logging in to icloud.com was then possible again and I was able to update all account information.