Ku qor sii wadida cutubkan - Mednis wuxuu kaalinta labaad ka galay 1955 Horyaalka Junior ee Adduunka ee ka dambeeyay Boris Spassky (labaduba waxay barbardhigeen ciyaartoodii). Wuxuu ahaa ciyaaryahankii ugu horeeyay ee ku guuleesta Bobby Fischer tartanka US Championship. Wuxuu ka ciyaaray kooxda Mareykanka ee 1962 ee Olombikada 15aad ee Chess
waxaana uu ku dhamaaday kaalinta saddexaad ee tartanka US Championship ee sanadihii 1961/62. Natiijooyinka tartanka waxaa ka mid ahaa kaalinta saddexaad ee Houston 1974, oo ku siman afaraad ee New York City 1980, iyo isla markaana ku siman Puerto Rico 1984. Xiriirka Puerto Rico Chess Federation, halkii uu ka ahaan lahaa Xiriirka Chess ee Mareykanka, ayaa si rasmi ah ugu soo jeediyay horyaalka Grandmaster. Wuxuu ka ciyaaray tartankii Interzonal ee 1979-kii magaalada Riga, oo ah meesha uu ku dhashay.