## Tuesday, December 17, 2013

### River crossing puzzle

There is a puzzle I heard a few years ago which goes like this.
Eight people want to cross a river.
They are A policeman and a criminal, a father and his two sons and a mother and her two daughters.
The trouble is that the boat they have can only carry 2 of them at a time and only the mother, father and policeman can row.
However the criminal will hurt anyone he is left alone with if the policeman is not there to restrain him. If the father is left with the daughters and the mother isn't there to protect them he will hurt them regardless of the policeman's presence. Similarly the mother will hurt the sons if she is left alone with them and the father is not there to protect them. How do they cross?

Here is an app with a much less creepily worded version of the problem. The policeman and criminal are replaced by a farmer and a dog. The father and his sons by a boy and his hamsters, the mother and daughters by a girl and her bunnies. Hurting by teasing.

Two related problems are the Jealous Husbands Problem and the Missionaries and Cannibals Problem

In the JH problem you have three husbands and there wives.  Everyone can row the boat but at no time may a wife be left without her husband and with another man. In the M+C there are three missionaries and three cannibals. Everyone can row the boat but you can never have the missionaries outnumbered by the cannibals on a particular bank.