Im not sure which way to answer this question, but I figured it out two different ways. First, 23 different states (DC included) have teams which have one the Division 1 Basketball championship. 12 states have two or more championships, meaning one two one two, or a combination of teams won. 8 states have two or more teams who have combined to win championships.
Since the above didn't fully answer the question as to which states, I'll do the honors. The following is for Men's Division 1 championship winners.
California (California, Stanford, San. Fran., UCLA) Kentucky (Kentucky, Louisville) Michigan (Michigan, Michigan St.) New York (CCNY and Syracuse) North Carolina (North Carolina, NC State, Duke) Ohio (Ohio St., Cincinnati) Pennsylvania (La Salle, Villanova) Wisconsin (Wisconsin, Marquette) If you want to do some research yourself, the link I used was: http://www.ncaa.com/history/m-basketball-d1.html
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