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Topic: General River Crossing (Read 2861 times) |
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kens
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General River Crossing
« on: Feb 4th, 2008, 11:51am » |
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X cannibals and Y anthropologists have to cross a river ( Y is greater than or equal to X).
the boat they have is only big enough for two people. if at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them. Give a generic way to solve this problem.
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Grimbal
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Re: General River Crossing
« Reply #1 on: Feb 5th, 2008, 1:26am » |
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Starting with the boat and all A's and C's on the left side.
While there are more A's than C's on the left side
A and C cross, C crosses back
At that point, we have at least 1 more A right than C's. Left, we have 1 A for each C.
Repeat
A and C cross, A crosses back, A and C cross, C crosses back.
It ends nicely with the last A and the last C crossing together.
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| « Last Edit: Feb 5th, 2008, 1:28am by Grimbal » |
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JiNbOtAk
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Re: General River Crossing
« Reply #2 on: Feb 5th, 2008, 3:19am » |
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What if A = C ? Is it solvable for N > 3 ? ( Maybe we would need a bigger boat )
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Grimbal
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Re: General River Crossing
« Reply #3 on: Feb 5th, 2008, 5:11am » |
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Oops.. I didn't see X can equal Y.
I think it still can be done up to 4 A's and 4 C's.
OK, 3 A's and 3 C's.
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| « Last Edit: Feb 5th, 2008, 5:21am by Grimbal » |
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JiNbOtAk
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Re: General River Crossing
« Reply #4 on: Feb 5th, 2008, 4:39pm » |
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Would 4 A's and 4 C's be possible, if the capacity of the boat is now 3 ?
In other words, would there always be solution for A = C, N > 3, B = N - 1 ?
*B = boat's capacity.
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Grimbal
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Re: General River Crossing
« Reply #5 on: Feb 5th, 2008, 10:30pm » |
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I think you need 2B-1 >= N.
So yes to your question.
PS: oops, in fact, B=4 is always enough.
So
N=3: B=2,
N=4, 5: B=3
N>=6: B=4
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| « Last Edit: Feb 5th, 2008, 10:34pm by Grimbal » |
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mad
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Re: General River Crossing
« Reply #6 on: Mar 3rd, 2008, 6:08am » |
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But, what is the algorithm in this case?
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Grimbal
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Re: General River Crossing
« Reply #7 on: Mar 3rd, 2008, 6:19am » |
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In which case?
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mad
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Re: General River Crossing
« Reply #8 on: Mar 3rd, 2008, 6:28am » |
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For any n and required b.
Is it the same as in the case of 3 cannibals and 3 anthropologists?
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| « Last Edit: Mar 3rd, 2008, 6:29am by mad » |
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Grimbal
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Re: General River Crossing
« Reply #9 on: Mar 3rd, 2008, 8:21am » |
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Yes, 3 cannibals and 3 anthropologists can be solved with a 2-seated boat, that's what I mean with
N=3: B=2
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mad
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Re: General River Crossing
« Reply #10 on: Mar 3rd, 2008, 9:19am » |
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on Feb 5th, 2008, 1:26am, Grimbal wrote:Starting with the boat and all A's and C's on the left side.
While there are more A's than C's on the left side
A and C cross, C crosses back
At that point, we have at least 1 more A right than C's. Left, we have 1 A for each C.
Repeat
A and C cross, A crosses back, A and C cross, C crosses back.
It ends nicely with the last A and the last C crossing together.
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I meant an algorithm of this type for any n and its required b.
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Grimbal
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Re: General River Crossing
« Reply #11 on: Mar 3rd, 2008, 9:25am » |
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For large N's you need a 4-seated boat. And in that case, the solution is obvious. Can't you see it?
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