One-Handed Basketball Player Gets a Shot With Florida By MIKE TIERNEY

“What did he do?” asked Milton Coach Matt Kramer.

Zach Hodskins, a senior guard, was hand-checking with both hands, the official explained.

“Hey,” Hodskins said, “I don’t even have two hands.”

Born without a left hand and forearm, Hodskins was thought to have a better chance to become president of the United States, as a relative imagined when he was an infant, than to play basketball for a college powerhouse. Yet Florida, which won back-to-back national titles in the past decade and reached the N.C.A.A. tournament’s Round of 8 the past three years, recently guaranteed him a roster spot for next season by designating him a preferred walk-on.

After people watch Hodskins sink 3-point shots, lunge for loose balls and unleash his unusual brand of play, what they notice almost as much as his missing hand is the chip on his shoulder. He has converted years of slights, perceived and real, into a continual source of energy that compels him to set lofty goals.

At nearly 6 feet 4 inches, Hodskins is a strong passer with extraordinary range. “He doesn’t have 3-point range; it’s in-the-gym range,” Kramer said. “Cross halfcourt, he’s in range after a dribble or two.”

Hodskins, who averaged 11 points a game last season and is averaging 6 points and 2.3 assists per game this season, would be assured significant playing time, perhaps even a starting role, at a lower-level college. But his nature made him accept the Gators.

“Zach wants the biggest challenge,” his father, Bob, said. “He has such an extreme desire to prove himself at the highest level he can.”

Bob and Stephanie Hodskins did not know that Zach would be born without half a limb. Early on, they pledged to rear him as they did his two older sisters — not that he would have tolerated any coddling.

“If you ever tried to help him up,” Bob Hodskins said, “he wouldn’t have wanted that.”

A daredevil from the beginning, Zach would climb out of his crib with a loud thud, alarming his parents.

Since then, he has dabbled in various sports, from skimboarding to triathlon.

Stephanie Hodskins yielded to one assumed limitation and bought Zach slip-on shoes to spare him laces. Yet he gravitated to shoes with laces, tying them at school as a sort of performance art on request.

When Hodskins locked in on basketball, his footwear of choice became high-top sneakers. He never hid an ambition to play in college, saying recently, “I never doubted myself, even though a lot of people did.” To them, he said, “Just watch.”

For every pickup-game captain who did not choose him and every Amateur Athletic Union program that did not invite him, Hodskins stockpiled motivation.

Concern that he was pushing himself too hard tempered his parents’ pride. Bob Hodskins would tape the calloused fingers on Zach’s right hand when they bled from marathon solo workouts.

“Dial it back,” his father would tell him. “You don’t have to prove yourself every day.”

Zach would hear none of it. “I love my competitiveness,” he said. “It got me to where I am today.”

In middle school, he went out for cross-country, primarily as conditioning for basketball. He promptly placed second in a meet that left him so exhausted his parents feared for his health. Zach’s explanation: “Allowing anyone to beat me was unacceptable.”

His parents removed him from the team. “We tried to tell him, ‘You can’t be perfect,’ ” Bob Hodskins said. “He expects to be so.”

The family found two A.A.U. coaches who helped Hodskins develop a repertory of moves, like a crossover dribble between the legs, to minimize the effect of his disability. Fine-tuning took place at gyms, playgrounds and, most often, the Hodskinses’ driveway. The continual thumping of the ball planted a nagging question: Would the investment pay off?

Zach’s parents never imagined how much it would. A year ago, a scouting service posted a one-minute clip of Hodskins’s highlights on YouTube that has nearly four million views.

Partly to ensure exposure to colleges, the family relocated from South Carolina last year so he could attend Milton, which had drawn scrutiny for the number of scholarship players it had. Just weeks after Hodskins enrolled, the team was barred from the postseason, and the coach was forced to resign after school authorities reported suspicions to the state athletics body that he was exerting “undue influence” on eventual transfers to Milton.

Hodskins will not receive a scholarship to Florida. But his parents were delighted by the message conveyed by Gators Coach Billy Donovan amid speculation on social media that the team’s offer bordered on a publicity stunt.

Bob Hodskins said Donovan had told the family: “We’re first and foremost recruiting you as a player. You are an inspiration, but you are here because you’re a good basketball player.”

(Florida, in accordance with N.C.A.A. rules, is not permitted to comment on walk-ons before they enroll because they have not signed with the team.)

Hodskins has not wavered from his oral commitment, though a call from the coach of a top program in Hodskins’s home state, Kentucky, might have given him pause.

Hodskins was celebrating his choice of Florida with schoolmates one night when his cellphone rang. It was Kentucky Coach John Calipari, who offered congratulations but not a uniform. Calipari also left a message with Hodskins’s father, who initially assumed it was a hoax.

Donovan did not specifically discuss Hodskins’s playing time, but the prevailing thought expressed by Bob Hodskins and Milton’s coach, Kramer, is, “I wouldn’t bet against it.”

Kramer added, “But if all he ever is is a really good practice player, he’ll be good for their program.”

Another endorsement came from Kevin Laue, the most recent, and perhaps only, significant N.C.A.A. Division I player with one hand.

“It’s really impressive what he can do on the court,” said the 6-foot-11 Laue, who graduated last year from Manhattan College and is the subject of a documentary, “Long Shot: The Kevin Laue Story,” which has aired in New York.

“It’s amazing to see what somebody went through, what I went through, to be on that platform,” Laue said, referring to a high-profile college opportunity.

Laue said his primary frustration was coaches who were not sure how to deal with a player without a limb and would set limits. As Kramer drove from Ohio to his new job at Milton this summer, he wrestled with how to coach Hodskins.

“I couldn’t visualize that situation fitting into a program that competes on a national level,” he said of Hodskins.

As the moving van was being unloaded at Kramer’s house, Milton players came by to help, none sooner than Hodskins.

“He wanted to be here first to make sure I would take him seriously,” Kramer said. “There was none of that ‘Treat me differently.’ ”

Kramer soon had his coaching template, with Hodskins as just one of the guys, doing push-ups and lifting weights on top of all his basketball tasks.

“He’s just a mean, nasty competitor — in a healthy way,” Kramer said.

The chip on his shoulder becomes evident when an opposing coach shouts, “Make him go left,” an order that once offended Hodskins’s mother.

Zach welcomed those words.

“I tell them, ‘Keep forcing me left.’ I get more separation when they do that,” he said.

Only once has he taken offense at an opponent’s words. An A.A.U. adversary whom Hodskins was outplaying shoved him and called him a profane name, preceded by “one-handed.”

Hodskins was stung, though not by the adjective, having come to terms with his disability so long ago that he jokes about it, as he did with the referee’s remark on his hand-checking.

Young people with disabilities, or their parents, have contacted Hodskins for advice and requests to meet, sometimes to shoot around.

“I welcome it, more than playing basketball,” he said. “Through basketball, I can reach out to those people. It’s a very humbling experience.”

It is upsetting, too, when he notices young people trying to disguise a disability with bulky clothing or cropped photos on their social media pages.

“I’ve never had that problem,” Hodskins said. “These kids need to be themselves, not hide it all their lives.”

As he proved to those who doubted him: “They never knew I’d get to this point. They didn’t know me.”