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# Travellers and Bridges

Mon 1 Sep, 2008 12:27 am
Part 1.
Six travellers approach a bridge together at night and their respective times for crossing the bridge are 1, 3, 4, 6, 8, and 9 minutes. What is the best way to schedule them to get all of them to the other side in the shortest time possible if there can at most two people per trip and there is only one lantern between them?

Part 2.
Seven travellers approach a bridge together at night and their respective times for crossing the bridge are 1, 2, 6, 7, 8, 9, and 10 minutes. What is the best way to schedule them to get all of them to the other side in the shortest time possible if there can at most three people per trip and there is only one lantern between them?

Note:
a) The maximum persons per trip is two in Part 1, and three in Part 2.
b) The slowest person crossing determines the crossing speed for that trip.
c) There is exactly one lamp which must be present with the traveller(s) for the entire duration of every crossing.
d) No memorising, throwing, pyromania or other nonsense is allowed.
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Robert Gentel

1
Mon 1 Sep, 2008 12:34 am
@Valedictum,
This seems so obvious that I even double checked the answer to see if there's some trick, but no it's just a riddle with an obvious answer.

1 minutes guy makes all the return trips for both riddles.
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Tryagain

2
Tue 2 Sep, 2008 07:53 am
If the answer is so obvious and it has been checked twice; why then do I not believe it to be true (for the first question)!

Well, for one… when you have eliminated the obvious, whatever remains, however improbable, must be the truth?

The times using Roberts’s fastest runner method:

3+1, 4+1 > etc. Total 34 minutes.

There are six men with crossing times 1, 3, 4, 6, 8 and 9 minutes and…
1 and 3 go across, 1 comes back: 8 and 9 go across 3 comes back; 1 and 6 go across, 1 comes back; 1 and 4 go across, 1 comes back; 1 and 3 go across.

Total time: 31 minutes.

Beat that Bob!
Robert Gentel

2
Tue 2 Sep, 2008 11:02 am
@Tryagain,
You are right, I had both my numbers wrong for some reason (the fastest runner way and the kill two birds with one stone way)
Tryagain

1
Thu 4 Sep, 2008 09:55 am
@Robert Gentel,
I hear you; I have those days…..every day.

May I assure the gentle reader no birds were hurt in the compilation of the answers.

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markr

1
Sun 9 Nov, 2008 11:48 pm
@Valedictum,
I get 37 for part 2.

1,2
1
9,10
2
1,2
1
7,8
2
1,6
1
1,2
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