For 30 years, one of Manhattan's most civilized pleasures was the Wollman Memorial skating rink, where skaters glided across the ice in a tree-shaded nook of Central Park with the midtown skyline as an elegant backdrop.

In 1980, the city closed the rink for what was to be a two-year repair job, estimated to cost $ 4.9 million.

Six years and $ 12.9 million later, in one of the most embarrassing fiascos in its municipal construction history, the city announced that the rink's new design had to be scrapped and work would begin again from scratch. Two more years and $ 3 million more would be needed to complete the job.

With a bird's-eye view of the rink from his office in the pink-marbled Trump Tower on Fifth Avenue, the city's flamboyant developer, Donald Trump, offered Mayor Edward I. Koch a bravado challenge. Reconstruction, "which essentially involves the pouring of a concrete slab," Trump wrote Koch last spring, should take no more than four months, and he would do the job himself. The city agreed.

Today, 3 1/2 months after he started, and $ 750,000 under budget, Trump, flanked by city officials, celebrated the opening of the three-quarter-acre rink as multicolored balloons floated skyward and schoolchildren chased each other across the ice.

"I guess it says a lot about the city, but I don't have to say what it says," Trump remarked tactfully.

Last week, Koch had called in his advisers to find out, as one put it, "how the city could spend six years and $ 12 million and not finish the rink when it took Trump only 3 1/2 months and $ 2.8 million."

At the rink today, the mayor had explanations ready. "There's much to be learned from the private sector," he said. Trump, he noted, is not hampered by city requirements to accept the lowest bidder. "He can hire the best," Koch said.

Nor is a private developer forced to adhere to the state's Wicks law, which requires state and city government agencies to hire separate contractors for construction, plumbing, electrical, and heating and ventilation work. "These contractors fall all over each other," Koch said. "No one is in charge of the other."

Besides, Koch added, Trump, who owns five buildings overlooking Central Park, "can tell these contractors, 'Look, you get this done on time and in budget or I'll never hire you again.' "

City officials and Gov. Mario M. Cuomo have tried to have the Wicks law repealed, estimating that it costs taxpayers $ 100 million a year, but the state legislature has succumbed to heavy lobbying by contractors and labor unions. The city was able to circumvent the law in the case of Trump's rebuilding the rink, by calling it an emergency contract.

To find the right contractor for ice-making equipment, Trump said recently, "I went to Canada. The city hired a contractor from Florida." But there were other feats of rinksmanship: Using 290 workers, Trump had the concrete floor of the facility poured in a single day.

The city, by contrast, had left 22 miles of delicate refrigeration coils uncovered for 13 months, due to contract delays. During that time, the coils were flooded by a stream and leaks developed. The leaks were not discovered until after concrete was poured over the coils. Then the city used jack hammers to break up the concrete, damaging more coils.

A report by the city comptroller last spring also found that construction began before design work was completed so that the cafeteria and lounge at the rink had to be redesigned in mid-project, causing a two-year delay. Trying to save energy, the city used a freon gas system alleged to be "state of the art" but later discovered to have multiple problems. Trump switched back to the traditional brine-water ice-making method.

The report found that a city subcontractor had diluted the concrete after underestimating the amount needed, and that contractors used a vibrating machine to pour the concrete that shook loose the joints of the refrigeration coils. When Koch commissioned a $ 200,000 consultant's study to find out what went wrong, the study took five months longer than expected.

One contractor died in a car accident. Another was found to have criminal connections.

While Trump, a 40-year-old billionaire, professes only charitable motives for his intervention, city officials note that he originally proposed to operate the rink and its restaurant at a profit, estimating $ 500,000 a year in revenues. Now Trump says any profit during the year he has agreed to operate it will go to charities such as cancer foundations. (Admission is $ 4.50 per adult, $ 2.50 per child.)

Meanwhile, after once being criticized when he tried to evict tenants from a parkside apartment building, Trump is reaping glowing publicity at a time when Television City, his proposed $ 2 billion West Side project that would feature a 150-story building, the world's tallest, is under city review.

However, for the 250,000 skaters expected to use the rink each season, with its burnished teak railings (a Trump touch), its exposed brick changing room with padded benches and its jaunty snack bar, motives hardly matter. "If the city couldn't do it, it was refreshing to see someone could," said Olivia Mann, a Columbia Grammar School teacher who brought her third-graders to skate today.

Joel Muhlstein, a Lane High School teacher who grew up in Queens, remembers going to opening day at the rink 30 years ago, when it was donated to the city by banking heiress Kate Wollman.

When the city bungled the repairs, "I wasn't terribly surprised," he said. "You see, I work for the city school system and they don't know what they're doing. But at least in this case they were big enough to admit they didn't know what they were doing."