Dog Crossing

Five people (A, B, C, D and Lisa) and five dogs (a, b, c, d, and Lisa's dog) are on a hiking trip. Each person owns one dog (the letters match). They come to a river and want to cross it. A rubber raft will hold up to three at a time, any combination of dogs and humans. Only the five people and Lisa's dog can drive the raft. How do you get them across the river? The catch: a dog cannot be in the presence of any humans unless its owner is also there. [Addendum: assume everyone exits the raft after each trip.]

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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