Clue: the country has a female President, respected worldwide, and previously active in fighting women's causes. Second clue: two of the country's recent heroes - one triumphant and sporting, the other journalistic and tragic - were, in fact, heroines, neither of whom became famous for staying at home.
The answer is Ireland, and the contradiction between question and clues tells a story. In one of Europe's most tenacious bastions of patriarchy, male privilege and conservative family values, something is stirring, mostly quietly, but occasionally with great emotion and noise.
To this day, the proportion of Irish women going out to work, 35 per cent, is among the lowest in Europe. But the number of young Irish women entering all forms of higher education and then going on into professions, such as medicine, accountancy and the law, has exploded in recent years to roughly half of the total (even more in the case of medicine). Fifteen years ago men comfortably outnumbered women in Irish universities; now women comfortably outnumber men. With the large and melancholy exception of inner-city unemployment, the Irish economy is boiling, especially for women. Three quarters of all the jobs created in Ireland in the past few years went to female applicants.
Carmel Foley, chief executive of the Employment Equality Agency, points to Mary Robinson's election as President in 1990 as a turning point. "Could I also point to Michele Smith [winner of three Olympic swimming golds] as having given a real boost to women in this country. Sport is so important, and this time we had an Irish woman - not Jack Charlton's boys - being cheered by the whole nation."(Veronica Guerin, the campaigning journalist also affected the whole nation when she was murdered by the gangsters she was investigating.)
Frances Fitzgerald, Fine Gael member of the Dail for Dublin South East, says there has been a "remarkable" transformation in women's attitudes in the last five to 10 years which cuts across education, income and class. "One of the most extraordinary developments has been the boom in women's involvement in self-help groups in inner-city areas. But there are also huge numbers of women besieging the adult education and retraining courses, even though the rules are sometimes stacked against them."
Ms Fitzgerald cautions, however: "When it comes to the real centres of power in Irish society - economics and politics - the real power is still predominantly in male hands, more so probably than in Britain or continental European countries."
In Eamon de Valera's vision of an austere, Church-obeying, inward-looking Ireland - enshrined in his 1937 constitution - Irish women were to be the homemakers and, before that, (in his own phrase) "comely maidens dancing at crossroads". The reality was sometimes quite different. Emigration meant a lack of husbands; prejudice meant a lack of jobs. The desperate country woman unable to find a husband, or the intelligent woman stuck in a loveless marriage to an oaf or a brute, are the staples of 20th-century Irish literature.
Many factors have conspired to breed rapid change, such asEuropean Union- inspired women's equality laws (until 20 years ago women were forced to resign from the civil service on marriage) and reverse emigration, which has brought many professional Irish women home.
But the most important single factor has been the weakening of the influence of the Church. The once absolute, Church-inspired ban on contraception has been gradually eroded since 1979, with the final restrictions on the public sale of condoms being lifted three years ago. Hence the most startling, and significant, statistic of all: the decline - even collapse - of the Irish birth rate, which has fallen by a third in 15 years to not much above the EU average. Families of five, six and seven children were still common in the last generation, but no longer.
Aisling O'Grady, 34, assistant dean of women students at University College, Dublin, spent eight years in London and came home two years ago. She says the atmosphere in Ireland - especially for women - has been "transformed". "There is a kind of fast-forward social revolution going on. The attitudes of the women students are light years from what I can remember even 15 years ago. In my day, many of the women students, especially the country girls, came to university to find husbands. Now they say they're not interested in marriage until their thirties. They're interested in careers."
The change has been so rapid that Finola Bruton, wife of the Taoiseach, John Bruton, got into trouble last year for saying more respect should be given to women who stay at home. She was roundly criticised by other women, including members of the Dail. This in turn produced a backlash from the anti-feminist women's groups which have also proliferated in recent years.
Among the leaders of this movement is Nora Bennis of Limerick, a founder of Mothers Working at Home and now of a new political party - the National Party. She intends to fight Limerick East at the next election, probably in the spring.
Mrs Bennis, a passionate, articulate mother of four usually pictured in the Irish media baking bread or ironing, insists she is not against women having careers. She opposes what she sees as the new psychological and financial pressure on Irish women to abandon their homes against their will. The social ills of modern Ireland - crime, drugs, teenage pregnancies - can be traced, she says, to the erosion of the traditional family. "I do think that the most important women's issue is motherhood. Not just for women, but for children and men also."
High-profile social battles over contraception, divorce and abortion have caused enormous controversy. But in other respects the increasingly unconstitutional activities of Irish women have - until recently - caused little stir. Carmel Foley at the equality agency reports an ugly rash of sexual harassment cases and a desperate shortage of child-care facilities, but on the whole the state of male-female relations is "very encouraging". She puts this down partly to the informality and "ease" between Irish people.
But Frances Fitzgerald believes this relative calm is about to be shattered. "You are going to see more politics on this issue, starting with next year's election. Patriarchies don't give up so easily."