I have heard of a famous problem called the "Wolf, Goat, and Cabbage Riddle" :(https://en.wikipedia.org/wiki/Wolf,_goat_and_cabbage_problem):
"Once upon a time a farmer went to a market and purchased a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?"
I have informally heard that this riddle can be seen as an optimization problem as it can be interpreted as a discrete optimization problem with integer constraints (i.e. certain combinations of items can not be left together). I have also heard that this riddle can appear in real life when there are thousands of objects and thousands of constraints (but I am not sure about this). It would be interesting to hear comments about this.
My Question: Does this "Wolf, Goat and Cabbage Riddle" have any relation to "Monge's Optimal Transport Problem"?
I am still trying to understand "Monge's Optimal Transport Problem" but in a general sense, it seems like this is related to the "Assignment Problem" seeking the "cheapest and fastest" way to transport items from one location to another location.
Is there any relationship between the "Wolf, Goat and Cabbage Riddle" and "Monge's Optimal Transport Problem"? Does (a more complex version of) the "Wolf, Goat and Cabbage Riddle" ever come up in real world Optimization Problems (e.g. scheduling and transportation)?