Source: A tutored student of John Knoderer's of www.MAZES.com on newsgroup rec.puzzles 9/14/97. I was later told it is related to an old Henry Dudeny puzzle.

Solutions were received from Robert T. McQuaid, Gregory Weidman, Denis Borris, and Philippe Fondanaiche, whose solution follows.

Let call l the Lisa's dog and let assume that everyone exits the raft after each trip. We have the following sequences: trip n° direction on the bank A on the raft on the bank B after trip (i odd) 1 ==> A,B,C,D,L,c,d l,a,b a,b 2 <== A,B,C,D,L,c,d l a,b 3 ==> A,B,C,D,L,d l,c a,b,c 4 <== A,B,C,D,L,d l a,b,c 5 ==> D,L,d,l A,B,C A,B,a,b 6 <== D,L,d,l C,c A,B,a,b 7 ==> C,D,c,d L,l A,L,a,l 8 <== C,D,c,d B,b A,L,a,l 9 ==> b,c,d B,C,D A,B,C,D,L,a 10 <== b,c,d l A,B,C,D,L,a 11 ==> d b,c,l A,B,C,D,L,a,b,c 12 <== d l A,B,C,D,L,a,b,c 13 ==> d,l A,B,C,D,L,a,b,c,d,l If we assume that a dog without its owner can pass a human who is not its owner only when the raft comes alongside, the number of trips is reduced to trip n° direction on the bank A on the raft on the bank B after trip (i odd) 1 ==> A,B,C,D,L,c,d a,b,l a,b 2 <== A,B,C,D,L,c,d l a,b 3 ==> A,B,C,D,L,d c,l a,b,c 4 <== A,B,C,D,L,d l a,b,c 5 ==> A,B,C,D,d L,l a,b,c,l 6 <== A,B,C,D,d L a,b,c,l 7 ==> D,L,d A,B,C A,B,C,a,b,c 8 <== D,L,d l A,B,C,a,b,c 9 ==> d D,L,l A,B,C,D,L,a,b,c 10 <== d l A,B,C,D,L,a,b,c 11 ==> d,l A,B,C,D,L,a,b,c,d,l Always with this last assumption, it's possible to make 6 humans + 6 dogs cross the river with 13 trips: The first 8 trips are the same as above. trip n° direction on the bank A on the raft on the bank B after trip (i odd) 1 ==> A,B,C,D,E,L,c,d,e a,b,l a,b 2 <== A,B,C,D,E,L,c,d,e l a,b 3 ==> A,B,C,D,E,L,d,e c,l a,b,c 4 <== A,B,C,D,E,L,d,e l a,b,c 5 ==> A,B,C,D,E,d,e L,l a,b,c,l 6 <== A,B,C,D,E,d,e L a,b,c,l 7 ==> D,E,L,d,e A,B,C A,B,C,a,b,c 8 <== D,E,L,d,e l A,B,C,a,b,c 9 ==> d,e,l D,E,L A,B,C,D,E,a,b,c 10 <== d,e,l L A,B,C,D,E,a,b,c 11 ==> L d,e,l A,B,C,D,E,a,b,c,d,e 12 <== L l A,B,C,D,E,a,b,c,d,e 13 ==> L,l A,B,C,D,E,L,a,b,c,d,e,l 7 humans + 7 dogs have to make 17 trips: trip n° direction on the bank A on the raft on the bank B after trip (i odd) 1 ==> A,B,C,D,E,F,L,c,d,e,f a,b,l a,b 2 <== A,B,C,D,E,F,L,c,d,e,f l a,b 3 ==> A,B,C,D,E,F,L,d,e,f c,l a,b,c 4 <== A,B,C,D,E,F,L,d,e,f l a,b,c 5 ==> A,B,C,D,E,F,d,e,f L,l a,b,c,l 6 <== A,B,C,D,E,F,d,e,f L a,b,c,l 7 ==> D,E,F,L,d,e,f A,B,C A,B,C,a,b,c 8 <== D,E,F,L,d,e,f l A,B,C,a,b,c 9 ==> D,E,F,d,e,f L,l A,B,C,D,L,a,b,c 10 <== D,E,F,d,e,f l A,B,C,D,L,a,b,c 11 ==> d,e,f,l D,E,F A,B,C,D,E,F,a,b,c 12 <== d,e,f,l L A,B,C,D,E,F,a,b,c 13 ==> d,e,f L,l A,B,C,D,E,F,L,a,b,c 14 <== d,e,f l A,B,C,D,E,F,L,a,b,c 15 ==> f d,e,l A,B,C,D,E,F,L,a,b,c,d,e 16 <== f l A,B,C,D,E,F,L,a,b,c,d,e 17 ==> f,l A,B,C,D,E,F,L,a,b,c,d,e,f,l With higher numbers of humans and dogs, it seems impossible to cross the river except if the raft can receive more than 3 at a time.

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