A farmer must transport a fox, goose and bag of beans from one side of a river to another using a boat which can only hold one item in addition to the farmer, subject to
the constraints that the fox cannot be left alone with the goose, and the goose cannot
be left alone with the beans. What is the fewest number of trips the farmer has to take
in order to transport all three safely to the other side of the river?
Show working using any appropriate mathematical representation(s)

The man in the goose cross the river, with the fox and the beans together, he leaves the goose on the other side and goes back across.

The man then takes the fox across the river, and since he can’t leave the fox in the goose together, he brings that goose back.

Again, since the goose and the beans can’t be left together, he leaves the goose and he takes the beans across and leaves with the fox.

He returns to pick up the goose and heads back across the river one last time.

Step-by-step explanation:

4 trips.

Step-by-step explanation:

The man and the goose across the river, leaving the fox and the beans together, he leaves the goose on the other side and goes back across.

The man then takes the fox across the river, and since he can’t leave the fox in the goose together, he brings that goose back.

Again, since the goose and the beans can’t be left together, he leaves the goose and he takes the beans across and leaves with the fox.

He returns to pick up the goose and heads back across the river one last time.

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