# River crossings(2)

The group of river crossing puzzles that I want to have a look at in this post is best characterized by its oldest specimen, that of the farmer, wolf, goat and cabbage. Chances are that you have a chicken instead of the goat, wheat instead of the cabbage or a fox instead of the wolf.

One form is:

1) a wolf, a goat and a cabbage*
A farmer bought a wolf, a goat and a cabbage at a market. On the way back home he has to cross a river. His small boat will hold, aside from him self, just one item.
If he leaves the wolf and the goat together, the wolf will eat the goat.
If he leaves the goat and the cabbage together, the goat will eat the cabbage.
How does he get everything across the river?
In all these puzzles there are no ropes, bridges or other tricks. Just play the ferryman.
You would disappoint me if you need a solution for this old traditional, but for the sake of completeness it is You can find the solution here

Like many river crossing problems it dates back the middle ages, and is found in the manuscript Propositiones ad Acuendos Juvenes, which is generally attributed to generally attributed to Abbott Alcuin.

The puzzle has been found in the folklore of African-Americans, Cameroon, the Cape Verde Islands, Denmark, Ethiopia, Ghana, Italy, Russia, Romania, Scotland, the Sudan, Uganda, Zambia, and Zimbabwe.[2], pp. 26–27;[7] It has been given the index number H506.3 in Stith Thompson’s motif index of folk literature, and is ATU 1579 in the Aarne-Thompson-Uther classification system.

In some parts of Africa, variations on the puzzle have been found in which the boat can carry two objects instead of only one. When the puzzle is weakened in this way it is possible to introduce the extra constraint that no two items, including A and C, can be left together.

2) One example of an extension with 4 items*
A farmer has to take a fox, chicken, caterpillar and crop of lettuce with his small ferry boat across a river. His small boat can hold 2 items aside from himself.
The fox would eat the chicken if they are left unattended.
The chicken would eat the caterpillar if left unattended
The caterpillar would eat the lettuce if unattended
How can he take everything across?
You can find the solution at here

That puzzle is rather simple, so we can easily expand it 1 item further:
3) 5 items*
A farmer has to take 5 items, a fox, chicken, spider, caterpillar and crop of lettuce with his small ferry boat across a river. His small boat can hold 2 items aside from himself.
The fox would eat the chicken if they are left unattended.
The chicken would eat the spider if left unattended
The spider would eat the caterpillar if left unattended
The caterpillar would eat the lettuce if unattended
How can he take everything across?
See Solution

As I told above, in Africa several regional variations have developed. Here is one 4) african variant*:
A young warrior returns to the village with a young lion, a young tiger and a young leopard. He must cross a small river, but his tiny canoe will only hold 2 items besides himself. Each of these animals will attack any of the others if left unattended. How can he take them all three across?
See Solution

There is a slightly more subtle way to extend the puzzle to 4 items. Serhiy Grabarchuk came up with this variation:
5) The fox, the goose, the grain, and the dog*
This time, the farmer has to transport a fox, a dog, a goose, and some grain across a river. He has a boat which can carry himself and either the fox, dog, goose, or grain. If the farmer isn’t present, the fox cannot be left with either the dog or the goose, or both. If need be, the goose can be left with the grain provided the dog is present because the dog will guard the grain and won’t eat the goose. Help the farmer cross the river.

(This puzzle is from The New Puzzle Classics by Serhiy Grabarchuk, Sterling publishing company, New York, 2005.)
The mouse, the elephant, the dog, and the cat

For yet another variation and a nice discussion of it, see The lettuce-fearing leviathan in the book A fine math you’ve got me into by Ian Stewart.
(the text above comes from http://www.mathfair.com/rvrcrossing.html).
You can look up the Solution

6) 2 wolves, a dog, a goat and a bag of grain
The may issue of Quantum also came with a small variation:*
A farmer was trying to cross a river in a boat which held him and two items. He had five items to transport to the other side: two wolves, a fierce dog, one goat and one bag of grain. When the farmer was not around, either wolf would eat the dog or the goat, the dog would eat the goat and the goat would eat the grain. How could the farmer transport all five items across the river?

You will find the solution as Solution 134

Some people at MIT took this puzzle type into space. The puzzles are all framed as characters from a cartoon science fiction series called Futurama.
Their puzzles are all placed in the future, with exotic names for stuff that, if you are not familiar with the series, you may find hard to remember. I prefer a translation into here-and-now things. Here we go, this is my contribution to the field:

7) 6 cargoes*
There are 6 cargoes to be transported over a river by boat from the southern to the northern shore.
The boat may hold 3 persons, including crew, and 1 cargo.
The ship starts at the southern shore.
The ship needs a 2 person crew. The only approved crew combinations are Bill and Bruce, and Lily + 1 other person.
The ship will make 6 trips to the northern bank and 6 trips back.
Not all persons and all cargo may be combined on the ship or on one of the river banks. See the conflict table below.
No one needs to leave the ship in order to pick up of drop of a cargo. Persons and cargo may be transferred simultaneously, so that a cargo is loaded on the ship while a person conflicting with the cargo disembarks at the same time, or vice verse.
At the end of the mission, all cargoes must have been transported to the northern shore. All persons must be back on the southern shore or on the ship.
There may be multiple crew combinations, but there is only one order in which the cargoes can be transported.
Starting positions:
Bill, Bruce and Lily: on the ship
On the northern shore: Alice, Mary, Peter, Quince.
All packages start on the southern shore.

Conflict table:

 Goose Cheese Guitars Cardboard Bananas Radios Persons Bill X X Bruce X X Lily Quince Alice X X Mary X X Peter X X Quince X X Lily

You can check the Solution 73

8) The pigs, peanuts and lilies*

You are at the planning desk of a small freighter cargo. Both John and Jack can handle the ship. Your transports are between Northport, Southport, and Island. The ship can handle either two persons or one person and one freight. The ship starts in Southport. And as you can guess, the ship needs at least one crew member.
a) Jack is on the ship in Southport. Jack is allergic for peanuts.
b) In Northport John is available. John is allergic for pigs.
c) In Northport there is a cargo of peanuts, which needs to go to the Island.
d) In Southport there is a cargo of pigs, which needs to go to Northport.
e) On the Island there is a cargo of lilies, which needs to go to Southport.

If someone is allergic to an object, he will not go ashore. He will go to a harbor with such a cargo, but will not leave the ship to pick up any cargo. Neither may, if a crewman is in a harbor, such a “toxic” cargo be dropped off in that harbor. There is only one gangway, so it is impossible that crewman A loads (resp. unloads) a cargo while crewman B, who is allergic to that cargo, leaves the ship (resp. boards it).
Roster the transports! What is the minimum number of shipments needed? It does not matter where the ship and the crew end.