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Solution to Problem 49
There were very many submissions to this week’s problem. The only correct solution
was sent in by Robert T. McQuaid. Way to go Robert!
The incorrect submissions all made the assumption  incorrect, it turns out  that
each man’s best strategy is to shoot at the other man with the better aim. However, as
R. McQuaid correctly observes, this is not the best strategy for Sir Soso; in fact, if
after drawing lots, Soso is to fire first, his best strategy is
to miss on purpose!
In every case, it is in Señor Casisiempre’s best interest to fire at Monsieur Toujours,
should Toujours still be a threat; similarly it is in Toujours best interest to shoot at
Casisiempre.
A straightforward check of probabilities gives the following table.
Firing Order
Survival Probability for
Toujours
Casisiempre
Soso
T  C  S
1/2
0
1/2
T  S  C
1/2
0
1/2
C  T  S
1/10
16/45
49/90
C  S  T
1/10
16/45
49/90
S  T  C
1/2
0
1/2
S  C  T
1/10
16/45
49/90
In order to compute these probabilities, you might start out by figuring the likelihood
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This note was uploaded on 03/01/2010 for the course MATH 301 taught by Professor Albertodelgado during the Spring '10 term at Bradley.
 Spring '10
 AlbertoDelgado
 Combinatorics

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