River Crossing Puzzles

The Farmer and his Cargo

A farmer is returning from market where he has bought a goat, a fox and a cabbage.

The farmer comes across river and finds a small boat that will hold only himself and another passenger. He can't leave the fox alone with the goat (the fox will eat the goat), or the goat with the cabbage (the goat will eat the cabbage). How does he get his cargo safely to the other side?

Answer

Take the goat to the other side of the river.
Go back alone.
Take the cabbage to the other side.
Bring the goat back.
Take the fox to the other side.
Go back alone.
Take the goat to the other side to finish.

Humans and Monkeys

There are three humans, one big monkey and two small monkeys that need to cross a river:

• Only humans and the big monkey can row the boat.
• At all times, the number of humans on either side of the river must be greater or equal to the number of monkeys on that side. (Or else the humans will be eaten by the monkeys!)
• The boat only has room for 2 (monkeys or humans).
• Monkeys can jump out of the boat when it's banked.

Answer

The Humans and monkeys should move as in the diagram below.

	Left Bank		Boat		Right Bank
Key: H = Human M = Big monkey m = Small monkey ---> = Moving to left bank <--- = Moving to right bank	HHHMmm
	HHHm	--->	Mm
	HHHm		M	<---	m
	HHH	--->	Mm		m
	HHH		M	<---	mm
	HM	--->	HH		mm
	HM		Hm	<---	Hm
	Hm	--->	HM		Hm
	Hm		Hm	<---	HM
	mm	--->	HH		HM
	mm		M	<---	HHH
	m	--->	Mm		HHH
	m		M	<---	HHHm
		--->	Mm		HHHm
					HHHMmm