A puzzling question: What is the most difficult piece when putting together a jigsaw? The first one, according to most enthusiasts.

So getting the right start probably will be the biggest challenge for the 750 participants in the fourth annual jigsaw puzzle competition this weekend in Athens, Ohio.

And these 750 puzzlers are not the only ones trying to piece together a big picture. Jigsaw puzzles, which have been around for more than 200 years, represent a $42 million-a-year industry in the United States alone.

"Heavy users, people who buy 10 or more puzzles a year, "have increased by 60 percent over the last three years," says Barbara Miller of Hallmark, manufacturer of Springbok puzzles and corporate sponsor of the National Jigsaw Puzzle Championship. This increase, combined with an overall rise in sales, she says, indicates a renewed interest in mind-oriented, family recreation.

When puzzle enthusiasts gather this weekend, however, they'll have more than recreation on their minds -- prizes range from $1,000 to $100. And there will be some familiar faces, including last year's singles champ, Joellen Beifuss of Memphis, who completed her 500-piece puzzle in 1:10:48 (the record: 59 minutes, 43 seconds), and the record-holding (1:38:57) doubles winners, sisters Lori Reeves and Lisa Heiser of Columbus.

Entrants, who pay their own expenses to compete in singles and doubles events, come from across the United States as well as several foreign countries. "Last year," says Miller, "we had contestants ranging in age from an 8-year-old to a woman from New Zealand, who refused to give her age but had to be in her seventies. She had been saving for two years to make the trip.

"We only have enough table space for 750 people, and the doubles event already is pretty much filled. We'll be encouraging some of the overload to compete as singles."

Singles pay a $10 entry fee, and doubles, $15. Singles competitors do 500-piece puzzles, doubles, 1,000-piece jigsaws. The semifinals take place at the Ohio University Convocation Center. Finalists move to the Dairy Barn Southeastern Ohio Cultural Arts Center.

"These competitions," says Miller, "really are family affairs," noting that both facilities are crowded with rooting fans and relatives as well as competititors.

Buddy Ward, 23, of Falls Church, and his doubles partner, 25-year-old Melody Patton of Portsmouth, Va., have been competing in the championships for the last three years. "We really have fun," says Ward, "win or not. The great thing about being there is people don't look at you like you have six heads. Anyone who does jigsaw puzzles would understand."

Ward, a computer programmer/analyst, and Patton, who works in the financial department of a hospital, met when they were students at Virginia Tech in Blacksburg, where they discovered their mutual interest in jigsaw puzzles.

"My grandmother loved puzzling," says Ward, "and she had me doing them by the time I was 5 or 6 years old. Melody lived in an off-campus apartment and she always had a puzzle going, so there we were."

Ward, a "heavy user" at 10 or 15 puzzles a year, says jigsaw puzzles are relaxing, adding, "You get a lot of self-satisfaction when you're done."

Nancy Hope, 50, of Clinton, qualifies even more impressively as a "heavy user." She explains, "They have a puzzle swap at the championships, and I plan on taking maybe 50 of my puzzles. I do at least 50 a year and so that way I may come away with a new year's supply."

Hope, who started doing jigsaw puzzles when she was about 10, says this, too, will be her third year at the championships. She competes as a single. "I'm married and have four children, ages 30 to 26, but I'm the only one that does the puzzles. They buy them for me but don't work them."

While he's "not fanatical enough to make it a criterion" for potential marriage partners, Ward says it isn't at all unusual to spend time jigsaw puzzling during a date. "I always have a puzzle going and, while I don't usually sit down and spend four hours at a time, I often work on a puzzle after work, while dinner's cooking."

Jigsaw puzzles provide a "healthy escape," agree some psychiatrists and other students of that other great puzzle -- the human mind. It's a natural means for forgetting one's everyday cares. The concentration required to work the puzzles tends to pull the player away from other, more mundane problems.

"People who don't work jigsaw puzzles regularly say it makes them nervous," says Hope. "I'm just the opposite. When I'm messed up, give me a puzzle and I'm just fine."

In bringing to bear their ability to visualize spatial relationships to solve jigsaw puzzles, world-class players are in good company. R. Chris Martin, a consulting psychologist for Hallmark/Springbok, notes that race-car drivers, airplane pilots, scientists, movie directors and video-game whizzes employ similar skills.

The old adage "When the going gets tough, the tough get going" seems to fit jigsaw puzzlers. They enjoy figuring out how to make ends meet. The tougher the jigsaw puzzle, it seems, the happier they are. Hope says one of her favorite puzzles is one that came out around the time of America's Bicentennial celebrations. A 1,000-piece challenge, "It's mainly red, white and blue and is filled with square and round presidential campaign buttons . . ."

Ward says one of his longtime favorites (he's had it for around 10 years) is known to jigsaw fanatics around the country. "It's called 'Little Red Riding Hood's Hood.' It's all red, with no variation in color whatsoever. I love it."