(FORTUNE Magazine) – If you were trying to explain the current contretemps at Virginia Military Institute to a fellow from Mars, you might plausibly begin with the late Howard Smith and his famous petard. Smith was the crusty Virginia conservative -- for some reason, liberals are not allowed to be crusty -- who for many years dominated the House Rules Committee. In 1964, he had this really neat idea. The House of Representatives was debating the Civil Rights Act, designed to end discrimination against blacks. Being opposed to the whole exercise, Smith decided to ridicule it: He added an amendment that extended the antidiscrimination laws to (gasp!) women. With virtually no serious debate, the House immediately accepted his amendment. By way of extending Howard's hoist and ensuring rapid rotation in his tomb, the U.S. Department of Justice is now demanding that women be allowed into VMI. It seems their exclusion violates the Civil Rights Act of 1964. VMI is an institution immortalized in the 1936 Broadway play (later a movie) Brother Rat. The term refers to the horrifying hazing undergone by the school's freshmen, who shave their heads and spend a lot of time in a ''rat line'' being harassed and humiliated for no good reason except to see if they can take it -- and a lot of them can't. Assuming, arguendo, that the Justice suit prevails, it will be great fun to see if the department next turns to filing sexual harassment suits by Sister Rats. But now we come to a fiendishly difficult question: In this age of boundless piety about sex discrimination, does any college in the country retain the right to admit just one sex? That right would clearly have disappeared if the equal rights amendment had passed. But what is the state of play with ERA kaput? Might the VMI suit ultimately represent a threat to traditional women's liberal-arts colleges like Smith and Hollins? The fact is that the fiendish question has never been settled. The Department of Justice itself says Smith and Hollins should relax. It says that VMI is being sued only because it is a government-supported institution. Says DOJ spokesperson Deborah Burstion-Wade: ''Private colleges are not a problem.'' But the public-private distinction is much less clear than it once seemed. The Supreme Court has firmly held that any educational institution whose students get federally insured student loans -- which means just about any college you can name, including Smith and Hollins -- is ''government- supported.'' That is, however, still not the end of the argument. Women's colleges may be exempt from the Civil Rights Act even if they do receive federal aid. The exemption appears to be lodged in Title IX of the Education Amendments of 1972. Title IX repeats the broad ban on sex bias in education, including college admissions, but then says the ban applies only to certain kinds of institutions (e.g., vocational schools), none of which sound like private women's colleges. A helpful lady at Smith College cites these words to show that private undergraduate liberal arts schools are in the clear. But wait: If Title IX is what gets you in the clear, then private women's colleges are not the only schools that have got there. Title IX offers certain other exemptions from the ban on bias, and one of them includes certain public colleges. ''In regard to admissions,'' it says, ''this ((ban on sex bias in admissions)) shall not apply to any public institution . . . that traditionally and continually from its establishment has had a policy of admitting only students of one sex.'' Why doesn't that cover VMI? Attorney General Mary Sue Terry of Virginia, who is fighting the Department of Justice suit, claims that it does. Your correspondent cannot get DOJ to state plainly why Title IX doesn't exempt VMI -- and if it doesn't, how can it exempt Smith and Hollins? One of these days, we hope to get a crisp answer to these questions. We also hope to discover why any nice young lady would wish to be on the rat line.