Rory McIlroy tracked an errant shot on the 10th hole at the Masters last year. (Andrew Redington / Getty Images)

What to do about Ginni Rometty, the chief executive officer of IBM?

That’s the sticky little problem confronting Augusta National as the Masters is set to begin next week. Rometty just happens to be a woman as well as the top executive at one of the tournament’s three corporate sponsors. These executives, in a tradition unlike any other, have always been extended membership invitations, but in another, more controversial tradition, the club has never had a woman member.

That’s a dicier call than the tee shot at No. 12.

“They have a dilemma on many levels,” Marcia Chambers, senior research scholar in law and journalist in residence at Yale Law School, told Bloomberg. “If there’s been a tradition of certain CEOs, then they should look at this new CEO in the same way. The only thing that makes her any different is her gender.”

Ginni Rometty, IBM CEO. (Andrew Harrer / Bloomberg)

There was such a stir over the matter in 2002 that Augusta decided to forgo commercial TV sponsorship in order to spare its sponsors pressure from women’s groups to stop affiliating with the club.

Billy Payne, Johnson’s successor, said in 2006 that there was “no timetable” for admitting women members and a Masters tournament spokesman declined to comment to Bloomberg when asked about the policy.

What should the Masters folks do about Rometty?