I refer to the “three of the four 20th-Century Presidents who ran for the office and lost” answer. Conceivably, there were six . Teddy Roosevelt was a 20th-Century President who ran and lost (though not as an incumbent). Nixon also would fit the vague category (though he lost before becoming a 20th-Century President).
The article would have been clearer had it been worded “three of the four 20-Century Presidents who ran to retain the office and lost.” The possibilities are, as indicated, Taft, Hoover, Ford and Carter.