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