Officials say gunfire erupted along 7th Avenue, between West 42nd and 41st streets, at around 11:50 p.m.
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The shooting happened in an area that is typically packed with people, and one that is a gun-free zone.
Video shows investigators combing through the scene in search for evidence. Authorities say they found four shell casings.
Police say this all happened when the three teens got into an argument with another person.
Two of the victims, a 15-year-old and an 18-year-old, were both shot in the thigh, officials said. They were taken to Bellevue Hospital in stable condition.
Authorities say a 17-year-old later showed up to Harlem Hospital with a gunshot wound to his arm.
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People walking by the crime scene pointed out that having designated gun-free areas do little to deter criminals.
"It's supposed to be no guns here, but it's New York. Some people might walk around with knives, weapons, whatever, pistols, everything. As you can see, obviously, no place is safe," one person said.
The suspect ran away from the scene and has not been arrested. Police say they believe the victims and suspect knew each other and that it likely wasn't a random act.
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