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27 replies to this topic

### #1 bushindo

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Posted 04 June 2009 - 09:30 PM

I promised final and adiace a break after their exemplary effort on Prisoner on a death row 8. Well, break's over.

There are 5 prisoners on a death row, call them A, B, C, D, and E. The warden gives them a chance to live. He gives them each a doctored gun and let them engage in a death match. Let's say the guns are modified so that their chances of hitting varies. A's chance of hitting and killing any other player is always 4/20. B's chance is always 7/20, C's is 10/20, D's is 13/20, and E's is 16/20. Assume that every single shot will either miss or kill.

The players shoot in this order, A, B, C, D, and E. Unlike Prisoners on a death row 8, prisoners don't have a choice of shooting anyone they want. Everyone must shoot someone right after him in the sequence. For example, A must shoot B, and if B is already dead, A must shoot C if C is alive, or go on to the next person if C is dead too. The person last in the sequence must shoot someone at the start of the sequence. So for instance, let's say it's E's turn, he must shoot A, or the next alive person at the start of the sequence if A's dead. The game continues until there's only 1 person left. The last person standing earns his freedom.

The warden likes you, so the night before the game he allows you to pick your position as A, B, C, D, or E.

1) What position should you pick?

Super hard bonus: What is the exact chance of survival for A, B, C, D, and E. Any method is allowed, but probabilistic method like simulation is not allowed since simulation provides an estimate of the rate but not the exact numbers. I'm not after the numbers, though. I'm looking for methods that would allow us us to compute the exact chance of survival. You don't have to implement the method, but you must describe it, and it must be doable within a reasonable amount of time.

Edited by bushindo, 04 June 2009 - 09:33 PM.

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### #2 perk8504

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Posted 04 June 2009 - 10:04 PM

My gut feeling is wanting to be C, gut with some real quick mental run downs of scenarios, but will need some time for the bonus and actually figuring out an answer I am confident in for picking the position too.
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### #3 icepick1346

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Posted 04 June 2009 - 10:06 PM

My gut feeling is wanting to be C, gut with some real quick mental run downs of scenarios, but will need some time for the bonus and actually figuring out an answer I am confident in for picking the position too.

I agree, but I won't be able to work the math till I get home later...
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Posted 04 June 2009 - 11:15 PM

Spoiler for I would choose

Edited by adiace, 04 June 2009 - 11:20 PM.

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Posted 04 June 2009 - 11:31 PM

Spoiler for I would choose

Spoiler for oops

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Posted 05 June 2009 - 12:05 AM

Spoiler for oops

Spoiler for back to

Edited by adiace, 05 June 2009 - 12:06 AM.

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### #7 final

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Posted 05 June 2009 - 12:31 AM

Spoiler for um

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### #8 James8421

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Posted 05 June 2009 - 12:32 AM

Spoiler for for part 1..

Spoiler for super hard part..

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Posted 05 June 2009 - 12:37 AM

Spoiler for Damn i keep flip floping

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Posted 05 June 2009 - 01:12 AM

Spoiler for Damn i keep flip floping

Spoiler for part 1

Edited by adiace, 05 June 2009 - 01:12 AM.

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