There is a riddle or puzzle that analyzes the options of three people
with guns, each of whom is in a position to kill the others.  (I just
watched "The Good, the Bad and the Ugly" and can't remember the
analysis of strategies.)  It might seem that the worst shooter should
aim for the best shooter, but my memory says that isn't the way the
analysis worked out.  Can you help?

Dear maxinebrooklyln-ga,

It is known as the Truel puzzle. According to the Brainyplanet article
referred to below, the earliest reference to puzzle is in Kinnaird?s
Encyclopedia of Puzzles and Pastimes (1946).

There are slight variations to the puzzle, so here below are some examples.

Article ?Truel in the sun.?
http://www.maa.org/mathland/mathtrek_1_26_98.html

Brainteaser Central
http://www.brainteasercentral.com/riddle.php?riddleid=648&status=a&PHPSESSID=11e504651b6cbeb90a618042ad2a3086

Everything2.com
Question
http://www.everything2.com/index.pl?node=old%20chestnut%3A%20truel
Answer
http://www.everything2.com/index.pl?node=answer%3A%20truel

Math Forum
http://mathforum.org/library/drmath/view/55662.html
http://mathforum.org/library/drmath/view/55630.html

Braingle
http://www.braingle.com/brainteasers/teaser.php?op=2;id=22672;comm=1


Brainyplanet which unfortunately does not give the set up of the
original problem which appears in the below book.
http://brainyplanet.com/index.php/Truel%20Solution?PHPSESSID=d799d1707bf6337c0547a1d6d275c326

Challenging Problems in Probability with Solutions (Paperback) 
by Frederick Mosteller 
http://www.amazon.com/gp/product/0486653552/104-2767448-8741565?v=glance&n=283155


I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder


Search strategy
"three men " shoot logic duel
Truel
://www.google.co.uk/search?hl=en&q=truel&btnG=Search&meta=

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Request for Answer Clarification by maxinebrooklyln-ga on 29 Jun 2006 04:02 PDT

Thank you for your answer, which is fine.  This is what I was looking
for in terms of the analysis I had read and forgotten.

However, I am sorry I didn't get back to Google Answers in time to ask
for clarification (I was waiting for an e-mail and forgot that there
is no e-mail notification).

It seems to me that the situation in "The Good, the Bad, and the Ugly"
is different from what the truel puzzle sets up in that 1) there is no
prescribed order of shooting, i.e., each shooter has the option of
shooting first, and 2) shooting into the ground isn't an option
because it would be a wasted shot since each shooter knows that he'll
either kill or be killed.

Is it possible to say under these conditions what each shooter's first
shot should be?  Specifically, if Blondie is the best shooter, Angel
Eyes is the second best, and Tuco is the worst, who should each one
shoot first?  Obviously the script writer had Blondie shoot Angel Eyes
first.

Thanks, Maxine Brooklyn

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Clarification of Answer by answerfinder-ga on 29 Jun 2006 06:27 PDT

I'm sorry Maxine, but I cannot help you on that. All the references I
found to to the problem have the participants taking their shots in
turn. None in which they all shoot at once. As for the film, I'm not a
fan of the genre and I saw it years ago and really cannot recall any
part of it.
Perhaps a more logically minded researcher may come up with a solution.
answerfinder-ga

I must take responsibility for not getting a completely satisfactory
answer because I didn't get back to the Google Answers web site in
time to ask for a clarification before the closing deadline.