When would-be apprentices apply to join the carpenters union, the first thing they have to do is take a math test. It's a sign of the increasing importance of math and computers, even in a traditionally low-tech field such as carpentry.

"You gotta know math," said Dave Dougherty, a 25-year-old third-year millcabinet apprentice. "Math doesn't lie."

Mr. Dougherty was operating a computerized beam saw for demonstration purposes yesterday at the annual carpenters' contest, held at the Carpenters' Training Center on Neville Island, while other apprentices showed off a CNC router, which can do complex engravings based on computer pictures.

"Every year, it seems like it gets more and more technical," said Rick Okraszewski, an instructor at the Carpenters' Training Center and an organizer of the contest. "The technology cuts manpower out, but we have to stay with it. We can't run away from it."

While Mr. Dougherty showed just what the beam saw could do, feeding wooden boards into the machine programmed to cut them into exact dimensions down to a thousandth of an inch, fourth-year apprentices were competing with each other in contests reflecting their specialties.

Floor coverers, for example, had to lay carpet, tile and linoleum around a wood square that included stair steps, while commercial carpenters had to build a wishing well and residential carpenters had to construct a doghouse. Those carpenters were first shown blueprints about half an hour before the competition began, and then given eight hours to complete their tasks.

The showcase event of the carpenters' contest is a collaborative "design-build" competition started six years ago in partnerships with the Pittsburgh Young Architects and the Master Builders Association.

The three person teams consist of one carpenter apprentice, one architect and one contractor. Two weeks before the competition, participants are given their task -- this year to construct a Disney-themed playhouse -- and the architect starts drawing up plans while the contractor gathers supplies in accordance with the predetermined budget.

For three hours Thursday night and eight hours yesterday, the carpenters took control to actually construct the structures, while the architects and contractors helped to paint Cinderella's pink and purple playhouse castle or lay the roof over Mickey Mouse's ears.

The design-build contest winners, carpenter Richard Clark, architect Jonathan Eggert of Edge Studio and contractor Jen Wisbon of Allegheny General Contracting, created a woodsy Winnie the Pooh hut that they finished about an hour before the other contestants.

The contest not only simulates the new "design-build" model in the construction industry, but also helps forge connections for graduating apprentices. In past years, three apprentices have gone on to work for contractors that they partnered with in the design-build competition, said Mr. Okraszewski.

"Whenever you talk networking, people think business," he said. "But we really have to network."

And these days, that networking can easily lead to jobs, thanks in part to a construction boom in and near Downtown. "I've been in this business 30 years," he said. "I've seen good times and bad times and right now, the market is very, very good."