Hungary competed at the 1924 Summer Olympics in Paris, France, returning to the Olympic Games after not being invited to the 1920 Games because of the nation's role in World War I.
Somfay took Hungary's only athletics medal in Paris, with the silver in the pentathlon.
Hungary and Italy split the individual bouts in their match, with eight apiece.
The foil team earned the country's first non-sabre fencing medal, winning the bronze.
Pósta and Garai were both in the three-way tie-breaker for medal placement, finishing first and third respectively.
Schenker finished fourth, and was also the only Hungarian man to compete individually in another weapon; he was eliminated in the first round of the foil.
Tary, representing Hungary in the women's foil competition, reached the final and placed sixth overall.
Hungary competed in the Olympic football tournament for the second time in 1924, losing their second-round match to Egypt.