The Feuding Hikers on the Bridge

Five hikers must cross a narrow bridge at night. They need 1, 2, 5, 8 and 12 minutes respectively to cross alone. The bridge holds at most two people at once, they must carry the single torch with them each time (it cannot be thrown), and a pair crosses at the slower member's pace. The hikers who take 1 and 2 minutes have fallen out: at no time may those two be alone together. That means they may not cross the bridge as a pair, and the pair may not be the only two people standing on either bank. What is the minimum total time, in minutes, for all five to get across?

• combinatorial games

Source: Original variation on the classic bridge-and-torch puzzle, written for AxiomIQ.