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According to the minimum time required for four people to cross the bridge, it can be concluded that the two people who use the least time will cross the bridge first, which will save them time to send lights back and forth.

So: (1) 1 2 minutes to cross the bridge first (it takes 2 minutes at this time).

(2) 1 minute, (it takes 3 minutes in total at this time).

(3)5 minutes and 10 minutes intersect (the total time is 2+ 1+ 10= 13 minutes).

(4) Come back in 2 minutes (it takes 2+1+10+2 =15 minutes).

(5) 1 minute 2 minutes to cross the bridge (the total time is 2+1+10+2+2 =17 minutes).

It took 17 minutes to cross the bridge at this time.

Answer: It takes at least 17 minutes for all four people to cross the river.