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For Bushindo - (others try at your own risk)


Best Answer Prime, 15 March 2013 - 10:19 PM

I am uncertain, what uncertain means in this context.

Cole's first shot strategy is clear. He must shoot himself in the foot thus exiting the duel with a non-fatal injury. (Hopefully, he does not miss.)

Spoiler for the honorable way

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18 replies to this topic

#1 bonanova

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Posted 15 March 2013 - 06:54 AM

A twist on the "truel" puzzle - a duel among three participants, where shots are taken in turn.
 
Alex always hits his man.
Bobby is not perfect, but he shoots better than Cole does.
The referee thus gives Cole the first shot, followed by Bobby and Alex in that order.
When a man is hit, he drops out [or drops dead].
The shooting continues in sequence until only one man is unhit.
 
Cole does not want to take Bobby out of the competition, then Alex will hit Cole. Game over.
But it may not be wise for Cole to hit Alex either. Cole is disadvantaged in an ordinary duel.
 
So Cole's first-shot strategy is uncertain.
Given that it is uncertain, what can we determine regarding Bobby's shooting accuracy?

Assume each knows the others' accuracy level.

 
Spoiler for translation

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 bushindo

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Posted 15 March 2013 - 04:45 PM

Probably not what you were looking for, but here's what I recommend Cole do
 
Spoiler for
 
So, clarification please. Can any participant choose to shoot into the air instead of the other duelists?

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#3 bushindo

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Posted 15 March 2013 - 10:14 PM

A twist on the "truel" puzzle - a duel among three participants, where shots are taken in turn.
 
Alex always hits his man. 
Bobby is not perfect, but he shoots better than Cole does.
The referee thus gives Cole the first shot, followed by Bobby and Alex in that order.
When a man is hit, he drops out [or drops dead].
The shooting continues in sequence until only one man is unhit.
 
Cole does not want to take Bobby out of the competition, then Alex will hit Cole. Game over.
But it may not be wise for Cole to hit Alex either. Cole is disadvantaged in an ordinary duel.
 
So Cole's first-shot strategy is uncertain.
Given that it is uncertain, what can we determine regarding Bobby's shooting accuracy?

Assume each knows the others' accuracy level.

 

Spoiler for translation

 

 

Assuming each participant is forced to shoot only at remaining duelists, then here's what I get

 

Spoiler for

 


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#4 Prime

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Posted 15 March 2013 - 10:19 PM   Best Answer

I am uncertain, what uncertain means in this context.

Cole's first shot strategy is clear. He must shoot himself in the foot thus exiting the duel with a non-fatal injury. (Hopefully, he does not miss.)

Spoiler for the honorable way


Edited by Prime, 15 March 2013 - 10:24 PM.

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Past prime, actually.


#5 bushindo

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Posted 16 March 2013 - 04:22 AM

 

A twist on the "truel" puzzle - a duel among three participants, where shots are taken in turn.
 
Alex always hits his man. 
Bobby is not perfect, but he shoots better than Cole does.
The referee thus gives Cole the first shot, followed by Bobby and Alex in that order.
When a man is hit, he drops out [or drops dead].
The shooting continues in sequence until only one man is unhit.
 
Cole does not want to take Bobby out of the competition, then Alex will hit Cole. Game over.
But it may not be wise for Cole to hit Alex either. Cole is disadvantaged in an ordinary duel.
 
So Cole's first-shot strategy is uncertain.
Given that it is uncertain, what can we determine regarding Bobby's shooting accuracy?

Assume each knows the others' accuracy level.

 

Spoiler for translation

 

 

Assuming each participant is forced to shoot only at remaining duelists, then here's what I get

 

Spoiler for

 

 

 

Okay, so earlier we found that not allowing an airshot on Cole's turn reduces to a trivial solution. So, let's assume that on the first shot, Cole has the option of shooting A, B, or none of those two.

Spoiler for


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#6 Prime

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Posted 17 March 2013 - 05:30 AM

Okay, so earlier we found that not allowing an airshot on Cole's turn reduces to a trivial solution. So, let's assume that on the first shot, Cole has the option of shooting A, B, or none of those two.

Spoiler for

Spoiler for correction


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Past prime, actually.


#7 bushindo

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Posted 17 March 2013 - 06:35 AM

Okay, so earlier we found that not allowing an airshot on Cole's turn reduces to a trivial solution. So, let's assume that on the first shot, Cole has the option of shooting A, B, or none of those two.

Spoiler for

Spoiler for correction

 

 

 

Indeed it should be a quadratic expression instead of cubic. My mistake. Good catch, Prime.


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#8 bonanova

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Posted 18 March 2013 - 04:37 AM

I am uncertain, what uncertain means in this context.

Cole's first shot strategy is clear. He must shoot himself in the foot thus exiting the duel with a non-fatal injury. (Hopefully, he does not miss.)

Spoiler for the honorable way

 

Yes, that is the answer. Nice job.

 

Spoiler for Analysis


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 bushindo

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Posted 18 March 2013 - 05:23 AM

I am uncertain, what uncertain means in this context.

Cole's first shot strategy is clear. He must shoot himself in the foot thus exiting the duel with a non-fatal injury. (Hopefully, he does not miss.)

Spoiler for the honorable way

 

Yes, that is the answer. Nice job.

 

Spoiler for Analysis

 

I believe the above solution conflates "trying to hit Alex" with "actually hitting Alex". Here is my reasoning

 

Spoiler for reasoning

 

Spoiler for 'minor point about notation


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#10 bonanova

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Posted 18 March 2013 - 06:48 AM

Spoiler for In English


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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