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Check this advice from Apple:

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...you might want to set up two-factor authentication instead. It's the best way to keep your account secure, and you won't need to remember any security questions. You can set up two-factor authentication right from your iPhone, iPad, or iPod touch with iOS 9 or later or your Mac with OS X El Capitan or later.

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copied from: If you forgot the answers to your Apple ID security questions - Apple Support

If necessary, if you are the original owner, take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store.

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or contact Apple ID Support. They will need to see the original purchase receipt/paperwork also.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat         

Apple Support using Twitter

Or fill out and submit this form.