More than a dozen bridges cross Pittsburgh’s three rivers, linking the North Side, the South Side, Lawrenceville, Oakland, Downtown and more. But can you cross them all, once and only once, and end up on the same side of the rivers where you started? How long would it take? And who would do such a thing? A group of coworkers from Duolingo set off in August to find out. The day-long hike all started with a conversation between Burr Settles, research director at the East Liberty-based language-learning app company, and Natalie Glance, vice president of engineering, about Leonhard Euler, an 18th century Swiss mathematician. Euler wanted to prove he could not once and only once cross all seven bridges of Königsberg in what is now Russia. “He realized he couldn’t do it and end up back where he started,� Settles said. In proving it impossible, Euler invented graph theory, which is now used in several sciences, including computer science. The bridge problem got Settles, of Morningside, wondering if a Eulerian circuit — crossing bridges to end up on the same landmass — could be done in 21st-century Pittsburgh. One Friday afternoon Settles shared a map he devised with Glance. It crossed 15 bridges over the course of 20 miles. Glance — who often walks her commute to Duolingo from Squirrel Hill and completed the 18-mile Rachel Carson Half-Challenge with a group of colleagues in June — joked she’d walk it with Settles. “It kind of snowballed from there,� Settles said. “If she hadn’t been pushing me, I probably would have just sat on the idea.� About 8 a.m. on a Saturday in August, the group and a plush owl met in Lawrenceville and set off. Duolingo’s mascot is an owl. Also, Eule, as in Euler, is German for owl, Settles pointed out in a blog post about the trek . The path Settles mapped started on the Lawrenceville side of the Washington’s Crossing Bridge and ended on the Glen Hazel side of the Glenwood Bridge. In between, it zig-zagged across the Allegheny, Ohio and Monongahela rivers. It crossed the 31st Street and 16th Street bridges and the Three Sisters bridges — Rachel Carson, Andy Warhol and Roberto Clemente. The group traversed the Fort Duquesne bridge and crossed the Ohio River over the West End Bridge. Along the way, they stopped in the Strip District for breakfast and at Point State Park to enjoy the scenery. The group summited Mt. Washington, lost a few members to the Shiloh Grill for lunch, and took the Duquesne Incline down to cross the Fort Pitt Bridge. “It is pretty amazing you get to see different parts of Pittsburgh on foot,� Glance said. “You realize how much of it you can traverse on foot.� After a stop in Market Square, the group crossed the Smithfield Street Bridge. Settles said he appreciated the bridge even more walking across it. Built in 1883, it is the second-oldest bridge still in use in the United States — behind only the Brooklyn Bridge, on which construction began 14 years earlier but opened two months after the Smithfield Street Bridge. The trek continued with more Monongahela River crossings over the Liberty and 10th Street bridges before a coffee break on East Carson Street, followed by a crossing of the Birmingham Bridge. After some navigating, the group made it down to Second Avenue and traveled a five-mile stretch of the Three River Heritage Trail before crossing the Hot Metal Bridge. During World War II, 15 percent of all American-made steel for the war effort crossed that same span from South Oakland to the South Side, Settles said. After following one-and-a-half miles on the Great Allegheny Passage, the Duolingo group stopped for ice cream at Page Dairy Mart before continuing the final two miles to its last crossing, the Glenwood Bridge. Three rivers, 15 bridges, 20.4 miles and 10.5 hours after they began, the group had completed Pittsburgh’s Eulerian circuit. “I know how to get on to all the bridges now,� Settles said, adding that some of the pedestrian staircases are tougher to find than others. “We probably wasted an hour to an hour-and-a-half doing that.� Settles said he enjoyed not only crossing the bridges, but seeing scenic parts of the city and noteworthy stops along the way. “We hit some highlights on the way of things that make Pittsburgh Pittsburgh, but you could probably do it in four hours if you were trucking,� he said. Duolingo employees are now considering routes Settles mapped out in New York City or Seattle, but those will be Eulerian paths, not circuits, since they cross the bridges but don’t end up on the same landmass. For anyone else attempting the same Pittsburgh route, Glance suggests good walking shoes and sunscreen, although the weather cooperated with the Duolingo co-workers during their hike. “Be ready to get a little bit lost,� she said. “Enjoy it.� Stacey Federoff is a Tribune-Review contributing writer. Email Newsletters TribLIVE's Daily and Weekly email newsletters deliver the news you want and information you need, right to your inbox.