There were wrestlers from Pennsylvania, bowlers from Illinois and skiers from Utah. There were two teams from the University of Maryland and four from the University of Oklahoma. Each team — 18 in all — had won an N.C.A.A. championship, and on Friday each arrived at the White House to be recognized by, and photographed with, President Trump.

Clemson’s football team had already made its visit, so Friday was for everyone else. And that made assuring that each team had its own space, and its own moment, a significant logistical challenge. The solution: Every team — the golfers and gymnasts, the triathletes and track stars — was assigned a spot, and the president met with each group in turn, following a prearranged path like a letter carrier completing a route.

He whacked a volleyball with the Ohio State men on the South Lawn, called attention to a Maryland lacrosse player wearing a Trump ’16 tie and mimicked a rifle with his hands as he approached West Virginia’s coed rifle team. On and on it went, first outside on a chilly morning, then inside through the East Room, the State Dining Room, the Red and Green rooms.

There were gifts — Oklahoma softball players brought Trump a personalized glove, and the Penn State women’s rugby team arrived with a jersey — but also two notable absences. The North Carolina men’s basketball team — whose coach, Roy Williams, has been publicly critical of Trump — begged off, citing a scheduling conflict.