Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough battery left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it's only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slowest needs 10 minutes to cross.

How do the campers make it across in 17 minutes?

  • $\begingroup$ When the flashlight is brought by someone on the bridge, does it light the whole bridge? $\endgroup$
    – leoll2
    Apr 21 '15 at 12:22
  • $\begingroup$ Not really, only the people who have the torch can see the bridge $\endgroup$ Apr 21 '15 at 12:32
  • $\begingroup$ Should the title be about 4 campers instead of 3? $\endgroup$
    – blakeoft
    Apr 21 '15 at 14:19

1 and 2 cross (2 minutes)
1 goes back with the flashlight (3 minutes)
5 and 10 cross (13 minutes)
2 goes back with the flashlight (15 minutes)
Finally, 1 and 2 cross together again (17 minutes)

The trick here is with the two slowest - you don't want to have to add both of their times on if you don't have to.


$1$ and $2$ cross together with the torch (takes 2 minutes)
$2$ goes back, bringing the flashlight (2 minutes)
$5$ and $10$ cross the bridge together, using the torch (10 minutes)
$1$ goes back with the flashlight (1 minute)
$1$ and $2$ cross the bridge with the torch (2 minutes)

Total: 17 minutes


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