Allenstown, N.H. — Political problem: You are one of the eight major Democratic candidates for president, but you are far behind. You don't have much money. You need to make a good showing in Iowa and New Hampshire. But time is running out. How do you get your share of the vote?
Solution: Besides the usual things (like advertising and debates), you also target specific groups, like Roman Catholics or women voters, with which you might have an edge over front-running Walter Mondale.
As the campaign here unfolds, key slices of the electorate are being courted: Young voters, elderly voters, and women by Gary Hart. Roman Catholics and conservatives by Reubin Askew.
It's a strategy that political analysts here say could help one or both of these candidates break out of the pack and pull down a surprising share of the vote on Feb. 28.
Recently, attention has focused on Senator Hart, whose well-organized team has waged a scrappy campaign from one end of New Hampshire to the other. Polls indicate that Hart's campaign has begun to catch fire, especially after the three-hour, televised debate Jan. 15 at Dartmouth College.
Meanwhile, Mr. Askew's low-key strategy to woo Catholics and conservatives may be making inroads in blue-collar areas like Manchester.
Here's a look at the campaigns of the two candidates, based on interviews with their state campaign directors and with political analysts across New Hampshire.
He is working hard for the female vote. As one woman, a Hart enthusiast, said after his umpteenth meeting here with women voters: ''I've seen more of Gary Hart here in the last three months than I have of my brother.''
Women are singled out by Hart for several reasons. Women, far more than men, are upset with Reagan policies. They are more fired up, more willing to work for a Democrat. Hart's policies mesh with those of many women voters on issues such as the arms race, pay equity, welfare, and the Equal Rights Amendment.
For awhile, Hart appeared to be making little progress here with women voters - or with anyone else. Critics suggested his appeal to women voters was condescending. But that perception has changed in recent weeks.
One could see Hart's strategy at work recently at a small Cape Cod-style home in North Concord. About 50 people, mostly women, had gathered to meet the senator. Many were single parents who had felt the sting of Reagan cutbacks.
The senator spoke for a few minutes about the arms race, about pay equity for women, and about his efforts in Congress to win better treatment for women on the job. Then for a few minutes he took questions, most of which focused on jobs and pay. And then he was gone, leaving behind the impression of a candidate who took these women and their problems very, very seriously.
Jeanne Shaheen, Hart's campaign manager in New Hampshire, points out that the senator hopes to win support among not only women, but also the elderly and younger voters. And she observes there is some important overlapping of these voter groups. Most elderly people, for example, are women, since women have longer life spans on average than men. And the Hart campaign has found that elderly voters are especially interested in new approaches to problems, which is the central theme of the Hart campaign.
Mrs. Shaheen also adds: ''If you look at where the candidates will be if they win, Walter Mondale's base is the whole white-male power structure of the Democratic Party. That is who will get first crack at top positions in a Mondale White House. Hart doesn't have these ties to the Democratic establishment.''
Polls show an interesting twist in New Hampshire this year. It's a twist that is ready-made for Governor Askew, who is far-away the most conservative candidate here. The polls show that Walter Mondale, the front-runner, has been doing as well with conservatives as with liberals. A December survey, for instance, found Mondale getting 50 percent of the conservative vote, and 42 percent of the liberal vote.
That points the way for Askew to cut into Mondale support. Further, his conservatism extends to the issue of abortion (he opposes it), which could give him a significant boost with Catholic voters.
Here in Allenstown the other day, this twin appeal to Catholics and conservatives could be seen. A freezing rain was falling, and travel conditions were next to impossible, but that didn't dissuade the Askew team from getting here, even though campaign manager Dick Bouley's little Renault Alliance skidded into a snowbank on the way.
Why such determination to attend a gathering of only 45 retired people? St. John the Baptist is a Roman Catholic Church in this blue-collar community just outside Manchester. New Hampshire has an unusually large number of Catholic voters, many conservative, who came here from Canada.
Donna Lou Askew, the candidate's wife, spent about an hour at the center. She shook every hand in the house, gave a short speech, and stayed for lunch with the group. She spoke of her husband's record as governor of Florida, his support for senior citizens, small business, and education, and his reputation for integrity.
If Askew can capitalize on the large bloc of conservative Democrats in this state, and add substantial Catholic support to that, he could be the sleeper candidate of this primary.
So far, Askew hasn't begun to move up in the polls. He's still down near the bottom. Meanwhile, the latest Boston Globe poll indicates Gary Hart's strategy is finally beginning to pay off. He's risen to 12 percent, up 4 points since December. Mondale remains out front (37 percent), but, perhaps significantly, he has fallen 12 percent in two months. Other standings: John Glenn, 18 percent (up 2); Jesse Jackson, 16 percent (up 10); George McGovern, 4 percent (down 1); Alan Cranston, 2 percent (down 2); Ernest Hollings, 2 percent (up 1).