I am paying college tuition for my grandsons who live in Virginia, I live in NC. Can I claim the tuition on my taxes

Q. Can I claim the tuition on my taxes?

A. No.

Where you and the student live is not an issue.

The education credit goes with the student's exemption (dependency). If you claim him; you claim the tuition credit. If his parent claims him, the parent  claims the credit.  If he claims himself, he claims the credit*. This is regardless of who actually pays for the tuition.  Although the general rule, in taxes, is that you must be the one making the payment, to get the deduction or credit, there is an exception for education. If nobody can claim him, or the parent's income is too high to claim the credit, and he doesn't have enough income to owe taxes, then the education credit is just lost*. 

*Technically there is a provision that allows a student-dependent to claim a federal tuition credit. But, from a practical matter it seldom works out.  A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he supports himself by working. He cannot be supporting himself on student loans & grants and 529 plans and parental or grandparent support.  It is usually best if the parent claims that credit.  

If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit.  The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)