# River crossings (4) – Bigamists

The puzzles in this post are extracted from the previous river crossing post, as that post grew too large. There is a common characteristic too these puzzles, though I find it hard to give an exact definition of this common property.

1) Bigamists
Back to the form of the puzzle with Jealous couples. M.G. Tarry has complicated the problem by assuming that the wives are unable to row. He also proposed a further complication by suggesting that one of the husbands is a bigamist traveling with both his wives.
Steven Kransz’s in his book: “Tecbniques of problem solving” gives a similar variation: “A group consists of two men, each with two wives, who want to cross a river in a boat that only holds two people. The jealous bigamists agree that no woman should be located either in the boat or on the river banks unless in the company of her husband.” That is how Miodrag Petković cites it in his book: Famous puzzles of great mathematicians. The latter condition makes it impossible to solve, and I guess that the latter condition should actually read “The jealous bigamists agree that no woman should be located either in the boat or on the river banks with the other man unless in the company of her husband.”
For the solution, see solution 121

2) A family affair
A recent addition tot his class of puzzles, which surfaced on the web as a flash game, is the following: A father and two sons, a mother with two daughters, and a thief guarded by a policeman want to cross a river. Their only means of transport is a raft able to carry 2 people. There are some problems:
• The Father is a rather nasty guy who will beat up the two girls if the mother is not present
• I regret to say that the Mother is equally nasty and will beat up the two boys unless the father is present
• The thief will beat up the boys, girls and adults if not accompanied by the police.
• Only the Father, the Mother and the Policeman know how to operate the raft
How many trips do you need to get them all across?
The site is in an Asian language, which suggests that the puzzle is of Chinese/Japanese or Korean origin. I welcome any information on the inventor of this puzzle. You can find it here.

You can find the solution at number 131

Actually this puzzle has a strong connection to both the elementary farmer-wolf-goat-cabbage puzzle and the bigamists puzzle.

3) The farmer, the kids and the pets.
Another recent flash based river crossing panel can be found at http://www.smart-kit.com/s888/river-crossing-puzzle-hard/>this site
The rules are simple:
A farmer, his son and daughter, and their pets need to cross a river. The pets are an aggressive dog, 2 hamsters, 2 rabbits. There is a small two-seater boat they can use. All 3 people know how to use the boat, but none of the animals can.

1. If the farmer is not around, the aggressive dog will bite everyone and everything.
2. If the daughter is not around, the son will tease the rabbits.
3. If the son is not around, the daughter will tease the hamsters.
4. The hamsters and rabbits get along fine with each other.

The solution is number 151

4 ) The two polygamists
Here is a new puzzle, which occurred to me while traveling by car today: Two polygamists, each accompanied by three wives, want to cross a river with a boat that can hold only 2 people at a time. The two men are so jealous, that they wont allow any of their wives to be in the boat, or on one of the riverbanks, with the other man unless he himself is present. An extra complication is that only one of the men, and one of his wives, can row.
How many crossings do they need?

You can find the solution at number 135