Four people want to cross a bridge. They all begin on the same side. It’s night time and they only have one flash light with them. At most two people can cross the bridge at the same time, and any party who crosses, either one or two people must have a flashlight with them. The flashlight must be walked back and forth not thrown etc. Each person walks at a different speed. A pair must walk together at the pace of the slower person.

One person needs one minute to cross, another needs 2 minutes to cross, another needs 5 minutes and another needs 10 minutes. How can all the people get across the bridge in 17 minutes?

call those person a,b,c, d

a and b go across: 2 minutes
b returns with flash: 2 minutes
c and d go across: 10 minutes
a returns with flash: 1min
a and b go across: 2 min

To solve this puzzle, we need to devise a strategy that allows all four people to cross the bridge in the shortest possible time, which in this case is 17 minutes. Let's break the problem down into steps:

Step 1: The two fastest people cross the bridge together
- The person who takes 1 minute and the person who takes 2 minutes cross the bridge together, using the 2-minute time since they must walk at the pace of the slower person.
- Total time elapsed: 2 minutes

Step 2: The fastest person goes back with the flashlight
- The person who takes 1 minute goes back to the starting point with the flashlight.
- Total time elapsed: 3 minutes

Step 3: The two slowest people cross the bridge together
- The person who takes 10 minutes and the person who takes 5 minutes cross the bridge together, using the 10-minute time since they must walk at the pace of the slower person.
- Total time elapsed: 13 minutes

Step 4: The second fastest person goes back with the flashlight
- The person who takes 2 minutes goes back to the starting point with the flashlight.
- Total time elapsed: 15 minutes

Step 5: The two fastest people cross the bridge together again
- The person who takes 1 minute and the person who takes 2 minutes cross the bridge together, using the 2-minute time since they must walk at the pace of the slower person.
- Total time elapsed: 17 minutes

All four people have now crossed the bridge in a total of 17 minutes, which is the minimum possible time.