Dr. John A. Vu

SJSU Computer Engineering Department

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Monthly Puzzler

Try and solve the puzzler and put it in my office
mailbox with name and contact number on it. If you
successfully get the correct answer along with a
detailed page of work, you'll be rewarded with
$25 in cold cash from me. Note: These problems tend
to be tedious, and could take hours to find the
correct answer.

 

Here's a puzzler for you all:  You and two of your friends
get into a dispute and decide to solve it with a "truel", a
three way duel.  Friend #1 is a crack shot, never missing
his target.  Friend #2 hits his target 2/3 of the time.  You
hit your target 1/3 of the time.  It is decided that you will
take the first shot, the 2/3 marksman will take the second 
shot (if still alive) and the 100% marksman will go last. 
This will continue until there is only one left alive.  On
your turn you get to fire one bullet.
 
You get to go first.  In order to maximize your chances of
living thru this, where should you take your opening shot?
And what are your chances of winning the truel if you
follow this strategy?