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When the listener contestant for the Who's Carl This Time? round couldn't figure out the answer to a question about Condoleezza Rice and asked for a hint, Mo Rocca sang "Blank-a-roni, the Secretary of State" (in tune of "Rice-a-Roni, A San Francisco Treat!"). Huge kudos to @Ojoya for tracking this one down for me!
During the Listener Limerick Challenge round when Peter was discussing the soccer/football matches between Muslims and LGBTs, Mo sang "everybody fatwah" to the tune of "Everybody Dance Now".