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Topic: River Crossing (II) (Read 586 times) |
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ThudnBlunder
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River Crossing (II)
« on: Jun 1st, 2003, 4:15am » |
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Three missionaries and three cannibals are trekking through the African jungle. They come across a river infested with crocodiles and they have one canoe which can carry only two at a time. All three missionaries and one cannibal know how to row. However, whenever the cannibals outnumber the missionaries on either side of the
river bank, they will eat make soup with them. How many trips are required for all of them to cross the river?
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| « Last Edit: Jun 1st, 2003, 1:49pm by ThudnBlunder » |
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TenaliRaman
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Re: River Crossing (II)
« Reply #1 on: Jun 1st, 2003, 7:30am » |
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Denoting missionaries as M1,M2,M3 and cannibals as C1,C2 and C3 and the banks as bank1 and bank2.
1> M1,C1 go to bank2
2> M1 returns to bank1
3> C2,C3 go to bank2
4> C3 returns to bank1
5> M1,M2 go to bank2
6> M2,C2 return to bank1
7> M2,M3 go to bank2
8> C1 returns to bank1
9> C1,C2 go to bank2
10> C2 returns to bank1
11> C2,C3 go to bank2
Problem solved (i think!)
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Icarus
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Re: River Crossing (II)
« Reply #2 on: Jun 1st, 2003, 11:01am » |
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One problem, TenaliRaman: Your method requires all three cannibals be able to row the canoe, but the problem states that only one knows how. So they are either going to have a crash course in canoeing, or come up with a different plan.
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TenaliRaman
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Re: River Crossing (II)
« Reply #3 on: Jun 1st, 2003, 1:25pm » |
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Hmm crash courses can be expensive , i would rather think of an alternative .....
Using the same notations as the last post.Assume C1 knows canoeing.
1> C1,C2 go to bank2
2> C1 returns to bank1
3> C1,C3 go to bank2
4> C1 returns to bank1
5> M1,M2 go to bank2
6> M2,C2 return to bank1
7> M2,C1 go to bank2
8> M2,C3 return to bank1
9> M2,M3 go to bank2
10> C1 returns to bank1
11> C1,C2 go to bank2
12> C1 returns to bank1
13> C1,C3 go to bank2
that was cheap now!!
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Chronos
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Re: River Crossing (II)
« Reply #4 on: Jun 1st, 2003, 1:40pm » |
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The key to these things is to never backtrack (i.e., undo the move you just did), and you'll find that your moves are usually forced.
So, let's see... Denoting rowers as capital, the first step must be either Mc, MC, or Cc. If we start with MC, then C can't come back, because then the missionaries on side 1 get et. So the next step would be M comes back. But that would mean that a missionary needs to make the third crossing, which means soup.
So our first step is either Mc or Cc, and either way, the rower comes back alone. We have MMMCc (boat) ~~~~ c. A missionary can't make the third trip, so it's got to be Cc, and C comes back: MMMC (boat) ~~~~ cc. At least one missionary needs to go across now, and he needs another with him for defense, so the next step is MM, and the only choice to come back is Mc. So now we have MMCc (boat) ~~~~ Mc.
OK, what can we do now? We must send MC or MM (since Mc is backtracking, and anything else requires a stewpot). But MM leaves us with Cc ~~~~ (boat) MMMc, a dead end. So the next step is MC, leaving us with Mc ~~~~ (boat) MMCc. And at this point, we see that we're in the mirror image of the previous step, so we can just flip our first steps around to finish.
To sum up:
MMMCcc (boat) ~~~~ (empty)
1: (Mc) -->
MMCc ~~~~ (boat) Mc
2: <-- (M)
MMMCc (boat) ~~~~ c
3: (Cc) -->
MMM ~~~~ (boat) Ccc
4: <-- (C)
MMMC (boat) ~~~~ cc
5: (MM) -->
MC ~~~~ (boat) MMcc
6: <-- (Mc)
MMCc (boat) ~~~~ Mc
7: (MC) -->
Mc ~~~~ (boat) MMCc
8: <-- (Mc)
MMcc (boat) ~~~~ MC
9: (MM) -->
cc ~~~~ (boat) MMMC
10: <-- (C)
Ccc (boat) ~~~~ MMM
11: (Cc) -->
c ~~~~ MMMCc
12: <-- (M)
Mc (boat) ~~~~ MMCc
13: (Mc) -->
(empty) ~~~~ MMMCcc
For a total of 13 crossings. I think, by the way, that only one of the missionaries needs to row, too, but I'm not going to work that one out now.
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otter
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Re: River Crossing (II)
« Reply #5 on: Jun 1st, 2003, 8:48pm » |
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I thought all the crocodiles were at the animal conference. 
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
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