It’s the question on everyone’s lips in philanthropy: Who is the mysterious donor giving away millions of dollars to at least a dozen colleges across the country?

A circle of successful businesswomen? A publicity-shy (or playful) billionaire? Oprah?

What’s so unusual is that not even the colleges themselves know the answer. But the parlor game is afoot, with only one real clue: So far, all the colleges are led by women.

Coincidence? Unlikely. With about 23 percent of U.S. college presidents women, the odds of a dozen randomly selected institutions all having female leaders are 1 in 50 million.

Melissa Berman, president and CEO of Rockefeller Philanthropy Advisors in New York, thinks the donor might be “a woman who maybe grew up in an era in which the opportunity to go to college was not taken for granted by women, and who feels that women in leadership positions are important motivators for women to be able to achieve their potential.”

Brian O’Rourke, director of development at Clemson University in South Carolina, imagines “a group of high-powered women that want to make sure women presidents in higher education are successful.”

“My gut tells me it’s a group of people sitting around saying, ‘Let’s just make a huge difference,'” he said. (Clemson has not gotten a contribution from the mystery donor.)

The gifts, ranging from $1 million to perhaps $10 million, and totaling up to $68.5 million so far, have arrived over the past seven weeks in similarly secretive fashion at colleges around the country, including Purdue in Indiana, Montclair State in New Jersey, and the University of Southern Mississippi. All were contacted by a law firm or other intermediary and given a highly unusual condition: College officials had to promise — in writing, in some cases — not to try to find out the donor’s identity.

The donations arrived in the form of cashier’s checks, or checks from law firms or other intermediaries. In most cases, the donor specified that the money be used for financial aid.

Michigan State University, which has a woman president, may be the 13th and latest recipient, announcing Thursday that it has been given an anonymous $10 million.

Philanthropy experts are thrilled but flummoxed. None knew of donors who had previously singled out colleges led by women. None could think of anything else the schools have in common.

“It could be this person wants to support female leaders of institutions of higher ed, but one then starts wondering why these and not others,” said Dennis Cross, vice president of university advancement at Washington & Lee University in Virginia, which is not one of the lucky recipients.

A few theories have popped up on Web sites, including talk show host Oprah Winfrey and someone connected with disgraced financier Bernie Madoff.

A spokeswoman for Winfrey said she was not the source. A representative for real estate baroness Leona Helmsley’s estate, which gave away $136 million Tuesday to hospitals, foundations and the homeless, also denied involvement.

The most plausible scenario seems to be that the money is coming from a “giving circle,” where a group of donors talk about their giving choices, and perhaps pool their money to invest, but decide individually where to donate. That would explain the eclectic list of colleges and the similar but not identical instructions they received.

“I could see a women’s giving circle … suggesting that it’s time for women to step up and fend for higher education at that level,” said Lauren Katzowitz Shenfield, principal of Philanthropy Advisers LLC in New York. But “I don’t get the anonymous piece.”