Quote:
Originally Posted by norway1456
Here goes:
A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a dark night and there is only one torch between them. Only two people can cross at a time.
Person A takes a minute to cross.
Person B takes 2 minutes to cross.
Person C takes 5 minutes to cross.
Person D takes 10 minutes to cross.
How do they all cross before the bridge collapses?
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A&B cross: 2 min
A comes back : 1 min
C&D cross: 10 min
B comes back: 2 min
A&B cross: 2 min
Total time: 17 mins.
The way to work it out is this. There must be three crossings and two crossings back. One of the crossings must take ten minutes. The two crossings back must take at least two minutes in total. That only leaves a maximum of five minutes for the remaining two crossings. If C is doing one of those crossings, that leaves no time for the final crossing.
Therefore, C&D must cross at the same time. But neither can come back, as that would use up more than the time available.
So, neither C nor D can do the first crossing, so A&B must, and one of them must come back. Then, since C&D must cross together, they must do the next crossing, and the other one on the far side must come back. And then A&B cross together again. Either A comes back first and B comes back second or vice-versa. It makes no difference to the overall timing.