Using this site means trees will be planted. River crossing puzzles are incredibly common, and popular in everything from puzzle books to pop culture works.

They pose fun little problems, which could take a while to figure out if you're missing a crucial element, but once you know the solution all of these puzzles become incredibly easy.

## Solving River-Crossing Puzzles with R

The riddle, in this case, goes as follows: A traveller is faced with a bridge, which they have to cross to get to where they wish to go. However, the traveller must bring their fox, chicken, and bag of grains to the other side as well, but the bridge is only strong enough to carry one of them at a time.

If the chicken is left alone with the grains the grains will be eaten, just as the chicken would be if the chicken was left alone with the fox. How does the traveller manage to make it across with the sack of grain and both of the animals? Jealous Husband Problem Three couples have to reach an island by boat. Unfortunately the boat can only carry 2 people at a time, and the husbands are so jealous the wives cannot be in the presence of another man while their jealous husband isn't present as well.

How do they cross? Without divorcing their overly jealous husbands of course. Bridge and Torch Problem There are 4 people who need to cross a bridge at night. Unfortunately they only have 1 torch left, which is absolutely needed to cross the bridge safely. There's only 15 minutes of burning time left on the torch, so they'll all have to cross in 15 minutes. Unfortunately only 2 people can cross it at a time.

Furthermore, person A can cross the bridge in 1 minute, person B in 2, C in 5, and D in 8. If two people walk together they'll walk as fast as the slowest person.

How do they all cross the bridge in 15 minutes? The problem in all of these tends to come when the second person, item, or animal has to be moved. If you move the chicken first, what do you bring next? If you bring one couple first, who returns with another husband or wife? The problem in the Bridge and Torch problem is slightly different, but I'll reveal the answer later. In the first two problems you do know some first moves are definitely the wrong one though.

You can't take the fox or the grain first for example. The solution is really simple, the problem is that most people forget they don't just have to stick to bringing something somewhere, they can also bring it back again later.

So the solution to the Fox, Chicken, and Sack of Grain problem could be as follows: - Bring the chicken across first. Pick up the grain, bring it across to the fox. In the Bridge and Torch problem the challenge lies in figuring out who to send together, and who to send back. But the solution is as follows: - Send A and B together.

## River crossing puzzles

Which takes 2 minutes. A then returns, taking another minute.Account Options Sign in. Top charts. New releases. Add to Wishlist. In this fun and challenging game, you will find a complete collection of all known river crossing logic problems, plus some completely new riddles that you will not find anywhere else. You may have heard about the farmer who must take a wolf, a goat, and some cabbage across a river, or a version featuring a fox, a goose, and a bag of beans.

Those are the classic river crossing puzzles. They are popular and well known, and they are all included in this game, along with many more new levels involving chess pieces, a farmer with cows and special levels designed only for geniuses. River crossing puzzles and their many variants represent ways of dressing up relatively straightforward mathematical problems. They invite attempts at a solution that range from trial and error to extensive mathematical analysis.

These puzzles are frequently used in job interviews. They are also taught to children in schools along with chess to boost their IQs and improve their critical thinking, mathematical problem-solving, and strategy development. Your goal in every level is to move all of the characters across the river while observing certain rules and restrictions. Once you have completed a level, you will receive one star for level completion. You can obtain an additional star if you finish the level in the minimum number of moves, and another if you finish the level in a set time that varies from level to level.

Try your best, work as quickly as you can, and keep your number of moves low to earn more stars. Your total number of stars will help you access more advanced levels. If you like playing chess and solving logic puzzles, then you are all set for new challenges. But unlike chess, you can play this game alone and have a lot of fun. Reviews Review Policy.

### River Crossing Challenge - Level 1

Improvements and Bug Fixes. View details. Flag as inappropriate. Visit website. See more. Logic Master 1 - Mind Twist. Weez Beez. Logic Master simply makes you smarter! Laurentiu Popa.This is one of those classic river-crossing conundrums which typically has only one answer. Yet, as with so many group initiatives, the value is found in the journey and not so much the destination. Given the discussion and critical-thinking required, I like to form lots of small groups of 2 to 5 people to tackle this puzzle.

In your set-up, either ask your group to imagine five primary elements — a woman, a rowboat, a chicken, a fox and a bag of corn — or provide some form of prop or toy to represent each. Explain that the woman has a dilemma — she needs to get the fox, the chicken and the bag of corn across to the other side of a river in as few moves as possible.

She has a rowboat, but it can only carry her and one other item at a time. Her dilemma is clear — she cannot leave the fox and the chicken alone together the fox will eat the chicken, and she cannot leave the chicken with the corn the chicken will eat the corn.

So, challenge your group s to identify a solution that gets all five elements safely to the other side of the river. How does the woman do it? To begin, the woman and the chicken cross the river together. The fox and corn are safe together. Once on the other side, the woman leaves the chicken and returns to the fox and corn. She cannot leave the chicken with the corn, so she leaves the chicken and rows the corn across the river and leaves it with the fox.

The key move of returning the chicken to the starting side even though it had successfully traversed the river may open lots of valuable discussion about the notion of taking two steps forward and one step back.

Or, the notion of making decisions for the greater good. Applaud their creativity and encourage them to find a solution, as hypothetical as it is. Like many group games and activities, it is hard to accurately track down the origin of this classic river crossing puzzle. If you happen to be aware of its origin, please let me know.

Contributor Mark Collard. Yes, I agree. A solution does not normally take too long, but the process of how each small group sorts through their solution is the most interesting.

Ideal for many teachable moments.Aside from the river, there is 1 policeman, 1 robber, 1 blond haired woman, and her 2 children and 1 red-haired woman and her 2 children. There is a boat having a carrying capacity of a maximum of 2 people. Only adults can sail but not the kids. Please help all people to move across the river, knowing that if the policeman is absent, the robber will kill all people there.

Step 3 : Now, Put one of the blond children B1 along with police in boat and sail to B. Step 4 : Drop B1 to island B and come back to island A along with policeman and thief. Step 9 : Put off red-haired woman RW back to island A.

Put thief and policeman back into the boat and sail to island B. Step 13 : Put one of the children of red-haired women R1 into the boat along with red hair women RW and sail to island B. Step 15 : Put thief back on island A and put last children R2 into the boat along with police and sail to island B.

Step 17 : Put thief back in the boat so that island A became empty and sail to island B. Step 18 : Here, you have reached island B with every person without breaking any of given the rule. Game Source : River Crossing. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Writing code in comment? Please use ide. Solution Steps: Step 1 :. Recommended Posts: Puzzle 1 How to Measure 45 minutes using two identical wires? Puzzle 2 Find ages of daughters Puzzle 3 Calculate total distance travelled by bee Puzzle 4 Pay an employee using a 7 units gold rod?

Load Comments.It seems incredible that we have gotten all the way to puzzle number 56 before including this all time favourite. It's fairly easy and many of you will have heard it before, that still doesn't mean there is nothing to learn:. A farmer is on his way back from the market, with him he has a fox, a chicken and some grain. When he reaches a river crossing he must use a small boat only big enough for him and one other item.

Unfortunately if the fox is left alone with the chicken it will eat it, as will the chicken eat the grain. Explain how the farmer can cross the river. Before reading the answer can I interest you in a clue? One of the reasons why this puzzle is easier than we're used to is that at every stage, basically every move available to you, other than reversing your previous move, if it's valid, is the correct move.

Lets take a look at the solution and then I'll explain what I mean- The farmer takes the chicken to the far side and leaves him there. The farmer returns in an empty boat and collects the fox or grain. At the near side he deposits the chicken and collects the grain or fox. At the far side he leaves the fox and grain together. He returns with an empty boat and collects the chicken. Seven crossing all done. So if we look at the first move, we can't take the fox, the chicken will eat the grain.

We can't take the grain, the fox will eat the chicken. All we can do is take the chicken. The only ambiguity is for example on the second move where I say ' collects the fox or grain. Again at each of these points if the move is legal it's the answer.

Exposition This puzzle exists in a lot of forms, I have chosen fox, chicken and grain. Other people talk about fox, goose and beans. Wolf, goat and cabbage.

Panther, pig and porridge. Or even some more exotics involving dragons and slaves. The premise is always the same, A can't be left with B, and B can't be left with C. Well for one these traditional puzzles are much more popular.

There's still stuff to talk about.The wolf, goat and cabbage problem is a river crossing puzzle. It dates back to at least the 9th century, [1] and has entered the folklore of a number of ethnic groups.

Once upon a time a farmer went to a market and purchased a wolfa goatand 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.

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? The first step must be to taken is to let the goat go across the river, as any other actions will result in the goat or the cabbage being eaten.

When the farmer returns to the original side, he has the choice of taking either the wolf or the cabbage across next. If he takes the wolf across, he would have to return to get the cabbage, resulting in the wolf eating the goat. If he takes the cabbage across second, he will need to return to get the wolf, resulting in the cabbage being eaten by the goat. The dilemma is solved by taking the wolf or the cabbage over and bringing the goat back. Now he can take the cabbage or the wolf over, and finally return to fetch the goat.

The puzzle is one of a number of river crossing puzzleswhere the object is to move a set of items across a river subject to various restrictions.

In the earliest known occurrence of this problem, in the medieval manuscript Propositiones ad Acuendos Juvenesthe three objects are a wolf, a goat, and a cabbage, but other cosmetic variations of the puzzle also exist, such as: wolf, sheep, and cabbage; [4] [2]p. The puzzle was a favorite of Lewis Carroll[10] and has been reprinted in various collections of recreational mathematics. Gurdjieff cites this riddle as "The Wolf, the goat and the cabbage". He notes, "This popular riddle clearly shows that In the Class of episode "Westley Side Story", Sunny and his students perform a similar exercise involving a chicken, a coyote and a sack of corn.

In the Bull episode "Justice for Cable", Benny begins a riddle with "a man has a fox, a duck, and a bag of beans". Bull inexplicably declares "There is no answer", and everyone believes him. 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 Ccan be left together. From Wikipedia, the free encyclopedia. Redirected from Fox, goose and bag of beans puzzle.River-Crossing Puzzles are a popular class of puzzles in the field of AI.

Many flavours of these puzzles exist. Here we use R to provide a somewhat generic framework to model and solve these type of puzzles. River-crossing puzzles are a type of puzzle where the objective is to move a set of pieces objects, animals or people across a river, from one bank of the river to the opposite bank, using a boat or a bridge.

What makes these puzzles interesting are the set of rules and conditions that apply. Typically the boat is only able to carry a limited number of pieces at any one go. Once upon a time, there was a Farmer who had a tiny boat. The boat was so tiny that it could only take the Farmer himself and one additional passenger.

He wanted to move a Wolf, a Goat and a Cabbage across a river with his tiny boat. When the Farmer is around, everyone is safe, the Wolf will not eat the Goat, the Goat will not eat the Cabbage. And of course he can only fit one more object with him on the boat either the Wolf, the Goat or the Cabbage. The question is: How can he safely transport the three of them to the other side of the river?

Solving river-crossing riddles entails starting with all pieces on one side of the river typically the left bank. This is the start state.

Then one considers all possible valid moves that can be done given the start state. These possible moves create a set of new states. The process repeats itself with the new states until we eventually arrive at the goal statei. To answer the above question we must build a graph of all possible valid moves. Thus we represent model the problem in terms of graph theory. Then we can apply a graph search algorithm to find all possible paths from the start node to the goal node, the shortest path smallest number of moves neededetc.

See the following video in order to apreciate the usefulness of this graph theoretic approach. And talking of graphs, the R language has some great packages for solving graph related problems and performing graph analytics. One such package that I have used a lot is igraph.

And I will be using this package in this blog to provide a solution to the river-crossing problems. But before we start working on the solution, it is worthwhile remembering that River-Crossing puzzles come in many flavours and varieties.

This website lists many of these. For example, there is the Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce puzzle where the farmer has to transfer 5 objects, but luckily for the farmer the boat is a bit larger can carry 3 pieces.

There are variants where a particular piece is repeated. Then there is the Japanese Family River-Crossing puzzle with its extremely complex rules. Also worth noting is the popular Missionaries-and-Cannibals problemfound in many AI text books. Actually river-crossing puzzles are in themselves just a subset of the class of wider puzzles called the Transport Puzzles. But this is beyond the scope here - we will just concentrate solely on river-crossing puzzles.

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