SALT LAKE CITY — At Northwestern, they’re celebrating a first-of-its-kind accomplishment — embarking on a trip to the NCAA Tournament that has eluded a school known for books, not basketball.

At Vanderbilt, they’re shrugging their shoulders — proving once again that smart guys can play hoops, too.

Welcome to the Brain Game — the NCAA’s plausibly deniable attempt at humor in the form of today’s matchup of “smart schools” in the West region.

The student-athletes from Northwestern (23-11) are seeded eighth and their counterparts from Vanderbilt (19-15) are ninth. Just as importantly, in this case: On the US News and World Report list of top national universities, Northwestern ranks 12th and Vanderbilt 15th.

“I wanted to have guys who wanted to be great basketball players and great students,” Wildcats coach Chris Collins said, in a way of explaining a turnaround that has taken the Wildcats to the NCAAs for the first time in 100-plus years of basketball. “To me, there’s no reason — why can’t you have both?”

No reason, really, as Harvard, Stanford, Princeton and, yes, Vanderbilt, have proven from time to time over the years.