# Three Wives & Their Jealous Husbands

Three jealous husbands with their wives, having to cross a river, find a boat without a boatman. But the boat is so small that it can contain no more than two of them at a time.

How can these six persons cross the river so that none of the women shall be left in the company of any of the men unless her husband is present?

(Women to row when absolutely necessary to prevent a violation of the above conditions).

Let the three husbands be A,B and C and their wives a,b and c respectively. The following moves are typical of a minimum solution with men rowing where possible.

Left Bank |
Crossing |
Right Bank |

ABCabc | – | – |

ACac | Bb ® | – |

ACac | ¬ B | b |

ABC | ac ® | b |

ABC | ¬ a | bc |

Aa | BC ® | bc |

Aa | ¬ Bb | Cc |

ab | AB ® | Cc |

ab | ¬ c | ABC |

b | ac ® | ABC |

b | ¬ B | ACac |

– | Bb® | ACac |

– | – | ABCabc |

Note that only a, B, and c need be able to row.

**The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing problems**

The missionaries and cannibals problem is a well-known toy problem in artificial intelligence

**Source of solution** – WIKIPEDIA

**Solving-**

Amarel devised a system for solving the Missionaries and Cannibals problem whereby the current state is represented by a simple vector <a,b,c>. The vector’s elements represent the number of missionaries on the wrong side, the number of cannibals on the wrong side, and the number of boats on the wrong side, respectively. Since the boat and all of the missionaries and cannibals start on the wrong side, the vector is initialized to <3,3,1>. Actions are represented using vector subtraction/addition to manipulate the state vector. For instance, if a lone cannibal crossed the river, the vector <0,1,1> would be subtracted from the state to yield <3,2,0>. 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. The five possible actions (<1,0,1>, <2,0,1>, <0,1,1>, <0,2,1>, and <1,1,1>) are then *subtracted* from the initial state, with the result forming children nodes of 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. The valid children nodes generated would be <3,2,0>, <3,1,0>, and <2,2,0>. For each of these remaining nodes, children nodes are generated by *adding* each of the possible action vectors. The algorithm continues alternating subtraction and addition for each level of the tree until a node is generated with the vector <0,0,0> as its value. 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.

**SOLUTION**–

The earliest solution known to the jealous husbands problem, using 11 one-way trips, is as follows. The married couples are represented as (male) and *a* (female), and *b*, and and *c*.

Trip number | Starting bank | Travel | Ending bank |
---|---|---|---|

(start) | a b c | ||

1 | b c | a → | |

2 | b c | ← | a |

3 | bc → | a | |

4 | ← a | b c | |

5 | a | → | b c |

6 | a | ← b | c |

7 | a b | → | c |

8 | a b | ← c | |

9 | b | a c → | |

10 | b | ← | a c |

11 | b → | a c | |

(finish) | a b c |

This is a shortest solution to the problem, but is not the only shortest solution

If however, only one man can get out of the boat at a time and husbands must be on the shore to count as with his wife as opposed to just being in the boat at the shore: move 5 to 6 is impossible, for as soon as has stepped out *b* on the shore won’t be with her husband, despite him being just in the boat.

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.e. not in the presence of any men on the shore), then this puzzle can be solved in 9 one-way trips:

Trip number | Starting bank | Travel | Ending bank |
---|---|---|---|

(start) | a b c | ||

1 | b c | a → | |

2 | b c | ← a | |

3 | c | ab → | |

4 | c | ← b | a |

5 | c | b → | a |

6 | c | ← b | a |

7 | bc → | a | |

8 | ← c | a b | |

9 | c → | a b | |

(finish) | a b c |

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »