Mathematical & Logical Puzzles -Q4

13. The Tribulations Of A Father Of Five

            A father rowing a boat, has to transport his five sons across a river in a minimum number of one-way crossings, such that finally all the children have had an identical number of crossings.

            The boat will hold the father (who does all the rowing) and not more than two children.  No pair of children of immediately neighbouring ages can be left together in the absence of their father or they will start to fight.  But children more separated in age will content themselves with more peaceful occupations.  What is more, the father, whilst handling the oars, is not able to control his children at the same time. 

            How does he get the five children safely across the river, in the minimum number of one-way crossings, so that each child has the same number of such trips?

14. 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).

15. Four Wives & Their Jealous Husbands

            Four couples have to cross a river with the aid of one small boat with the capacity of only two people.  Nowhere, either on land or in the boat, is any woman allowed to be left in the company of any of the men unless her husband is present.  How can the transfer be executed if there is an island in the middle of the river where the boat may land and leave some of its cargo?

16. Getting The Nuggets Across

            During the Alaska gold-rush, three prospectors who had struck it rich had to cross the Yukon.  But they could find only a small row-boat with the capacity of either two men or one man and a bag of gold nuggets.  Each of them owned a bag of the precious metal but the contents of each of the three bags of nuggets were not the same.  Smith’s gold was worth $8000, Jones’ $5000HHis and Brown’s $3000. 

            None of them trusted the other two, and so after some argument they agreed that the passage should be arranged so that none of them, either on shore or in the boat should be in the presence of nuggets worth more than he owned.  How did the men proceed to get themselves and their properties across the Yukon in the least number of crossings consistent with the restrictions?


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