Answer to
old chestnut: missionaries and cannibals:
They can cross the river as shown in the following schematic. M = missionary, C = cannibal, {} = boat.
MMMCCC {}
MMMC -> {CC}
MMMC {} CC
MMMC {C} <- C
MMMCC {} C
MMM -> {CC} C
MMM {} CCC
MMM {C} <- CC
MMMC {} CC
MC -> {MM} CC
MC {} MMCC
MC {MC} <- MC
MMCC {} MC
CC -> {MM} MC
CC {} MMMC
CC {C} <- MMM
CCC {} MMM
C -> {CC} MMM
C {} MMMCC
C {C} <- MMMC
CC {} MMMC
-> {CC} MMMC
{} MMMCCC