3 missionaries and 3 cannibals

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3 missionaries and 3 cannibals

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Three missionaries on the left side of a river and three cannibals on the right side of the river want to cross a river using a boat which can carry at most two people, The boat is on the cannibals side. Under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals if they were, the cannibals would eat the missionaries.

The boat cannot cross the river by itself with no people on board. Plan minimum number of trips in such a way that all the cannibals go to the left side and missionaries come to the right side without any bloodshed. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.

AI Search to Solve the Missionaries and Cannibals Problem

Asked 2 years, 5 months ago. Active 2 years, 5 months ago. Viewed 1k times. Jamal Senjaya. Jamal Senjaya Jamal Senjaya This problem has them on opposite banks and needing to trade places. Active Oldest Votes. JS1 JS1 Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

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3 missionaries and 3 cannibals

Question feed. Puzzling Stack Exchange works best with JavaScript enabled.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute to sign up. In the Missionaries and Cannibals problem :. Three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks and the boat, if there are missionaries present on the bank or the boatthey cannot be outnumbered by cannibals if they were, the cannibals would eat the missionaries.

The boat cannot cross the river by itself with no people on board.

3 missionaries and 3 cannibals

The shortest solution for this puzzle has 11 one-way trips. What should be the strategy to solve this puzzle for M missionaries and C cannibalsgiven that M is not less than C, or else the puzzle wouldn't be solvable.

For the case of M being more than Chere's an algorithm to transfer 1 missionary and 1 cannibal at a time:. And then you're left with the case of M-1 missionaries and C-1 cannibals on one side of the river. Just keep repeating this procedure it works by induction until you have only missionaries on the left side of the river.

Then you're home free. There's no way to get a similar arrangement for anything greater than three, because you can't send enough missionaries at once to balance out the rest of the cannibals.

For the case of more M than C it becomes trivial as a canibal can run the ferry after some initial setup. The M takes the boat back and gets another M, leaving C Ms on the original shore, The Ms get to the other side and send the C back with the boat.

3 missionaries and 3 cannibals

The C can now ferry alternating C's and Ms without issue. The Ms will always outnumber the number left on either shore. If M is 2 or more higher than C, then M can actually run the boat as well since they can start with 2 Ms in the boat and keep a higher number on both shores simultaneously while also operating the boat.

One missionary and one cannibal cross to the other side, The cannibal gets out and the missionary comes back Missionary gets out of the boat, two cannibals get in and cross One cannibals gets out and the other cannibal goes back The cannibal gets out and two missionaries get in and cross One missionary gets out, the other missionary stays in the boat and one cannibal gets in and goes back. The cannibal gets out and two missionaries get in and cross The two missionaries get down and the cannibal gets in the boat and goes back One cannibal gets in and they both cross but only one cannibal gets out The other cannibal in the boat goes back, collects the other cannibal, they cross and they get out.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Strategy to solve the Missionaries and Cannibals problem Ask Question. Asked 5 years, 11 months ago.

The Missionaries And The Cannibals

Active 3 years, 11 months ago. Viewed 34k times. John Bupit John Bupit 1, 1 1 gold badge 11 11 silver badges 29 29 bronze badges. I've never heard a solution to the problem for four missionaries and four cannibals. May 15 '14 at The first reference is to an article that probably answers the question very nicely, but it is behind a paywall.

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Active Oldest Votes. For the case of M being more than Chere's an algorithm to transfer 1 missionary and 1 cannibal at a time: Bring 1 missionary and 1 cannibal over. Bring 1 missionary and 1 cannibal over again. Joe Z.Menu toggle. Riddle Archives.

The Missionaries And The Cannibals. Riddle: There are 3 missionaries and 3 cannibals that need to cross a river.

There is only 1 way across the river and that is by boat. There is only 1 boat and only 2 people at a time may cross the river in the boat. You cannot have more cannibals than missionaries on one side of the river or else the cannibals will eat the missionaries and you fail.

How can you get all 3 missionaries and all 3 cannibals across the river in one piece? Answer: This is the 12 step process for completing this brain corker. I will call the starting place side A and the destination side B. And that's all there to it! A lot of people think it's impossible but it's really simple when you use the right logic. Riddle Quizzes. School Riddles. Take the School Riddles quiz!

A collection of riddles with a school theme. Great for the playground or classroom. Print riddle quiz or download PDF. Take Quiz. Kids Riddles A to Z. Kids riddles for each letter of the alphabet A-Z.

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Play as a riddle game or use as a fun classroom riddle quiz! How many can you answer? Download a PDF or print.GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. If nothing happens, download GitHub Desktop and try again.

If nothing happens, download Xcode and try again. If nothing happens, download the GitHub extension for Visual Studio and try again. Missionaries and cannibals is a classic artificial intelligence puzzle The code in this repository will work for all the different solutions for missionaries and cannibals problem. There are three missionaries and three cannibals on one side of a river bank consider left bank.

Move all the three missionaries and three cannibals on other side of a river right bank. There is one boat used to cross the river. This boat can take minimum one and maximum two persons at a time in each move. Any number of moves are allowed. Constraints: Missionaries cannot be less than cannibals on any of the bank. If so, then game will exit and goal will not be achieved. Skip to content.

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Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Sign up. Missionaries and cannibals is artificial intelligence problem. Jupyter Notebook Python. Jupyter Notebook Branch: master. Find file. Sign in Sign up. Go back.On one bank of a river are three missionaries and three cannibals.

There is one boat available that can hold up to two people and that they would like to use to cross the river. How can the boat be used to safely carry all the missionaries and cannibals across the river? The initial state is shown to the right here, where black triangles represent missionaries and red circles represent cannibals.

This problem can be solved by searching for a solution, which is a sequence of actions that leads from the initial state to the goal state. The goal state is effectively a mirror image of the initial state.

The complete search space is shown in figure 1. Figure 1: Search-space for the Missionaries and Cannibals problem. Arrows in figure 1 represent state transitions and are labelled with actions, e.

The initial state is shown again on the left, whereas the goal state is all the way to the right. MissionariesAndCannibalsApp is a Java application that explores the above search space using a number of uninformed search strategies.

Download the application and double-click it. Alternatively, run the command "java -jar MissionariesAndCannibalsApp.

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Either should bring up a window that looks essentially like the one shown in figure 2. Figure 2: The window of the application. To search for a solution, first select a search strategy.

Next, there are some configuration options for the search process. If the search space is to be searched as a graph, multiple paths leading to the same node will usually only be explored once.

The Missionaries And The Cannibals

In a tree, search states that can be reached by multiple paths will also be explored multiple times. The number of states to be generated can be limited to the given value, resulting in the search being abandoned at that point. For a depth-first search it is also possible to set a depth limit, meaning no states at a greater depth will be explored. The operation performed by a search engine consists of selecting a current search node and generating its successors, and the trace reflects this process.

For example, the line:. The number 11 in the example is the unique identifier for the search node. Note that there may be multiple nodes that contain the same state, especially when tree search is performed.

Then there is a description of the selected state which can be read as follows: on the left bank L: there are no missionaries 0m and one cannibal 1cand on the right bank there are 3 missionaries 3mtwo cannibals 2c and the boat b. Other states follow the same pattern. The lines following this one in the trace describe the successor states that have been generated, for example:. Even with tracing off the window will display some information about the search which is not part of the trace.The problem is specified like this.

On one side of a river, there are three missionaries and three cannibals.

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There is a boat which can be used to transfer people from one side of the river to the other. No more than two people can fit in the boat and it must have at least one person in it during any transfer.

The problem is to find the shortest sequence of transfers which gets all six people from one side to the other without ever creating a situation where missionaries outnumber cannibals on either side of the river. The idea being that if this happens, the missionaries will then be able to corrupt the cannibals by 'converting' them.

To solve this problem satisfactorily, your program must explicitly identify all of the optimal i. Well, there are different varieties of search which can all be used, such as breadth first, depth first, or iterative deepening. Each of these different search methods has different properties such as whether a result is guaranteed, and how much time and space is needed to carry out a search. This article uses breadth first search, as this search method is guaranteed to find a solution state.

Search is generally concerned with looking for a solution, or solutions in a search space of individual search states. Typically, a search space is a list or some sort of collection which contains each of the states that is to be checked to see if it is a solution state. A breath first search relies upon the basic search principles mentioned above.

What is of specific interest, is how the breadth first search actually goes about looking for a solution state.

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To illustrate this, consider the following diagram, where each of the ovals is an individual state:. It can be seen from the diagram above that there are a number of states, but how did the search choose which ones to look at for a given solution? With a breadth first search, each state at a given layer is expanded before moving to the next layer of states.

In the diagram above, it can be seen that the root state was expanded to find the states A1, A2, and A3. There were no more states at this level, so A1 was picked and expanded, which yielded A1. However, A2 and A3 must also be expanded before looking at these new states A1. If there are no more states at the current level to expand, the first node from the next level is expanded, this carries on until a solution or solutions is found.The missionaries and cannibals problemand the closely related jealous husbands problemare classic river-crossing logic puzzles.

In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals if they were, the cannibals would eat the missionaries.

The boat cannot cross the river by itself with no people on board. And, in some variations, one of the cannibals has only one arm and cannot row. In the jealous husbands problem, the missionaries and cannibals become three married heterosexual couples, with the constraint that no woman can be in the presence of another man unless her husband is also present.

Under this constraint, there cannot be both women and men present on a bank with women outnumbering men, since if there were, these women would be without their husbands. Therefore, upon changing men to missionaries and women to cannibals, any solution to the jealous husbands problem will also become a solution to the missionaries and cannibals problem. The vector's elements represent the number of missionaries, cannibals, and boats on the wrong side, respectively.

The state would reflect that there are still three missionaries and two cannibals on the wrong side, and that the boat is now on the opposite bank. To fully solve the problem, a simple tree is formed with the initial state as the root. Any node that has more cannibals than missionaries on either bank is in an invalid state, and is therefore removed from further consideration. For each of these remaining nodes, children nodes are generated by adding each of the possible action vectors. This is the goal state, and the path from the root of the tree to this node represents a sequence of actions that solves the problem.

The earliest solution known to the jealous husbands problem, using 11 one-way trips, is as follows. This is a shortest solution to the problem, but is not the only shortest solution. As mentioned previously, this solution to the jealous husbands problem will become a solution to the missionaries and cannibals problem upon replacing men by missionaries and women by cannibals. In this case we may neglect the individual identities of the missionaries and cannibals. The solution just given is still shortest, and is one of four shortest solutions.

If a woman in the boat at the shore but not on the shore counts as being by herself i. An obvious generalization is to vary the number of jealous couples or missionaries and cannibalsthe capacity of the boat, or both. If the boat holds 2 people, then 2 couples require 5 trips; with 4 or more couples, the problem has no solution. A simple graph-theory approach to analyzing and solving these generalizations was given by Fraley, Cooke, and Detrick in If an island is added in the middle of the river, then any number of couples can cross using a two-person boat.

The first known appearance of the jealous husbands problem is in the medieval text Propositiones ad Acuendos Juvenesusually attributed to Alcuin died In Alcuin's formulation the couples are brothers and sisters, but the constraint is still the sameā€”no woman can be in the company of another man unless her brother is present. From the 13th to the 15th century, the problem became known throughout Northern Europe, with the couples now being husbands and wives.

3 missionaries and 3 cannibals

The problem was later put in the form of masters and valets; the formulation with missionaries and cannibals did not appear until the end of the 19th century. Cadet de Fontenay considered placing an island in the middle of the river in ; this variant of the problem, with a two-person boat, was completely solved by Ian Pressman and David Singmaster in From Wikipedia, the free encyclopedia. The Mathematical Gazette.

Michie, Donald ed. Machine Intelligence. Archived from the original on March 8, In Stock, Oliviero; Schaerf, Marco eds. Lecture Notes in Computer Science. Stuttgart: Franz Steiner Verlag. Shaw, Lynne C. Cannibals and missionaries. New York: Association for Computing Machinery. Science News.


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