Four walkers and one torch on a narrow bridge

Four people must cross a bridge at night. They take $10$, $5$, $2$ and $1$ minutes respectively to cross. At most two can be on the bridge at once, they have one torch that must be carried on every crossing, and a pair moves at the slower person's pace. What is the least total time to get everyone across?

17 minutes. Send $1$ and $2$ over ($2$), $1$ returns ($1$), $5$ and $10$ cross together ($10$), $2$ returns ($2$), then $1$ and $2$ cross ($2$): $2+1+10+2+2=17$. The key is letting the two slowest share one crossing.