Kuhn cut himself on a knife that was sticking out of a box he was moving, which kept him from hitting the field on Saturday, The Star-Ledger reported.
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"He is a thick body; powerful young man who I think will put some more weight on and he will be able to squat in there and do a nice job inside," Giants coach Tom Coughlin told reporters after rookie minicamp practice Saturday. "He has a very, very interesting story. It was nice to talk to him a little about that in terms of -- he has played club football in Germany -- small teams -- 20 guys on a team and that kind of thing. He certainly did an outstanding job at N.C, State. I just wish we could have gotten to see him a little bit out here."
In his last season at North Carolina State, Kuhn collected 45 tackles, including 9.5 for a loss, and 4.5 sacks.
"It was only six years ago that my father and I were traveling the East Coast with a DVD highlight tape, asking small colleges like Liberty University if they wanted to give me a chance," Kuhn told the New York Post on Friday.
"To be standing here now and talking about being just the second native of Germany to be drafted in the NFL is pretty remarkable, I would say," Kuhn told the Post.
Kuhn first began playing football in Germany, which is one of 62 countries governed by the International Federation of American Football, with the Weinheim Longhorns.