Answer to old chestnut: wolf, goat, and cabbage:

The answer is shown schematically in the diagram below, in which W = wolf, G = goat, C = cabbages, F = farmer, and {} = the boat.


FWGC {}
WC            -> {FG}
WC                              {} FG
WC               {F} <-            G
FWC  {}                            G
W             -> {FC}              G
W                               {} FGC
W                {FG} <-           C
FWG  {}                            C
G             -> {FW}              C
G                               {} FWC
G                {F} <-            WC
FG   {}                            WC
              -> {FG}              WC
                                {} FWGC

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