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In the head-to-head matchup, they argued over who has flip-flopped more, who has the better friendship with Israeli Prime Minister Benjamin Netanyahu and who has spent less time in Washington.

“The only reason you didn’t become a career politician is you lost to Teddy Kennedy in 1994,” Mr. Gingrich told Mr. Romney as the candidates squared off for the latest debate in Des Moines, Iowa, Saturday.

Mr. Romney acknowledged that was true, but said losing that Senate race to Mr. Kennedy “was probably the best thing I could have done” because he stayed in the private sector and learned the lessons he said prepared him to run for president.