1. The fox, chicken, and lettuce. Someone pointed out to me that it's usually stated as fox, chicken and corn. Well, sure, if you like your puzzles to make sense. :-)
Bring across the Chicken.
Come back with nothing.
Bring the fox across.
Take back the chicken.
Bring the lettuce across.
Bring the chicken across one last time.
2. Three missionaries and three cannibals. This one was solved by Secret Squïrrel. For those who didn't know, I give free linkage to the first solver of any puzzles. I appreciate it when other people write up the solution so I don't have to.
mmm ccc || nobodyI leave it as an exercise to the reader to find out how many missionaries and cannibals you can safely bring across if you have a boat that holds three people.
mmm c || cc (2c ->)
mmm cc || c (<- 1c) mmm || ccc (2c ->)
mmm c || cc (<- 1c) m c || mm cc (2m ->)
mm cc || m c (<- 1m1c) cc || mmm c (2m ->)
ccc || mmm (<- 1c) Now the c come across in 3 trips.