Dear Xerxes-ga
A Carroll diagrams is simply a logic table which allows us to record
which pairings of logical events are true or untrue. If there is some
restriction on what logical combinations are allowed, then we can make
deductions from filling in such a diagram.
Carroll diagrams are used by mathematicians, and taught to children in
school these days. They are also used by Electronics Engineers who
prefer to call them "Karnaugh Maps", after the Engineer who first
described their use in the analysis of digital logic.
Those of us who are habitual puzzle solvers regularly make use of such
diagrams. Often, the puzzle setter will provide the diagrams needed in
order to save the solver the trouble of creating one.
The particular puzzle you have set is very complex. To understand the
concept of Carroll diagrams, we need to look at a simpler puzzle.
Take the puzzle and associated diagram at:
http://www.woogly.com/logic.htm
(It's a little way down the page).
The first piece of information is that Aunt Agatha is not travelling
to Bermuda or Nova Scotia - so we can put an "N" for No in the boxes
where Aunt Agatha intersects with those destinations.
Putting a "Y" or and "N" in various boxes for all the clues given, and
understanding the underlying premise (in this case that each Aunt will
only visit one destination, departing on one date etc.) will allow us
to solve the puzzle, as enough values will be revealed to fill in the
whole diagram.
In solving the puzzle you set, it is not really possible to make much
use of Carroll diagrams, as there are too many interdependent
variables, and the puzzle is solved in multiple little stages, each of
which doesn't really need a diagram. I found it helpful to create a
chart with each "over" on it, but although that helps, such a chart is
not strictly a Carroll diagram. At every stage you need a good
knowledge of the rules of cricket, which either makes the puzzle
extremely entertaining, or quite impenetrable, depending on your
viewpoint.
It is fairly simple to work out who bowls which overs. From that there
follows a sequence of deductions, most of which flow from the limited
number of ways in which each bowler's runs total can be achieved, and
the fact that the strike can only be exchanged in an over where a
single is scored.
The solution given in the comment made by Adamc is exactly correct,
and rather than repeat it here (it is quite long), the link is given
below, and I thank Adamc for his assistance.
Websites:
The full solution to the puzzle:
http://groups.google.com/groups?hl=en&lr=&safe=on&selm=385acf7b.1287002%40news.zipworld.com.au&rnum=2
Explanation of Carroll Diagrams:
http://www.maths.uwa.edu.au/~gregg/Seminars/1997SemII/PureMathsStudentSeminars/week4.html
How to solve logic problems using Carroll Diagrams:
http://www.geocities.com/Heartland/Plains/4484/logic.htm
The Official Rules of Cricket (especially useful for American
puzzlers!):
http://www-rsa.cricket.org/link_to_database/NATIONAL/ICC/RULES/
Google Search:
The following search gives many sites containing logic problems which
can be solved using Carroll Diagrams:
://www.google.com/search?sourceid=navclient&q=logic+problems
Best Regards,
david_uk-ga |
