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Seven states have no Republican representatives in the U.S. House of Representatives:
University of Minnesota Twin Cities +1
Connecticut
Delaware
Hawaii
Massachusetts
New Hampshire
New Mexico
Rhode Island
In the U.S. Senate, Democrats and Independents hold all seats in these states as well.
University of Minnesota Twin Cities
Note: Vermont is a similar edge case. While it has zero Republican representatives, its lone U.S. Senator, Bernie Sanders, is an Independent rather than a Democrat.