Facebook rolled out the red carpet for Michael Sayman when the social network hired him for a job that started last month, including flying him out to meet Chief Executive Officer Mark Zuckerberg. Sayman, 17, brought his mom along on the trip. The position Facebook recruited him for: summer intern. “When I got the e-mail saying — oh my god — Mark Zuckerberg wants to meet you, I had to make sure nobody was playing a prank on me,” Sayman, who wears braces and recently graduated from high school in Miami, said in an interview. “It was just incredible to be able to meet him.” Landing top talent is getting so tough in Silicon Valley that technology companies are trying anything for an edge — including hiring interns out of high school and boosting new recruits’ perks. Facebook said it just started wooing interns before their freshman year of college, while LinkedIn opened its summer program to high schoolers two years ago.