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

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