Author Topic: The Truel  (Read 228 times)

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Offline pianodwarf

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The Truel
« on: January 18, 2012, 01:22:31 PM »
This is a logic puzzle I first read in "Games" magazine when I was a kid.  The solution is all over the web, of course, and some of the regulars here have probably heard it before -- let's give others a chance to try to figure it out before anyone posts the answer, though.

You, Mr. Goode, and Mr. Best have been having a heated dispute over a matter of great consequence, and not being able to come to a resolution, you've decided to settle the matter with a duel -- or, more precisely, a truel, since there are three of you.  However, you've also decided that since you're all gentlemen, you're going to try to kill each other like civilized people.

The three of you are each going to take turns firing, one at a time.  The truel will continue until there is only one survivor.  You are the worst marksman of the three, hitting your target only 33% of the time.  Mr. Goode is a better shot, hitting his target 66% of the time.  Mr. Best, however, never misses -- he hits his target 100% of the time.  (For the sake of simplicity, we will assume that a hit is a kill.)

In an attempt to level the playing field somewhat, you all agree that turns will be taken starting with the worst marksman first, then proceeding to the next best marksman, and so on.  This means, of course, that you're the one who starts the truel.

Who do you aim at with your first shot?
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn

Online Dante

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Re: The Truel
« Reply #1 on: January 18, 2012, 01:26:40 PM »
Yourself. :o
Actually it doesn't. One could conceivably be all-powerful but not exceptionally intelligent.

Offline pianodwarf

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Re: The Truel
« Reply #2 on: January 18, 2012, 01:32:37 PM »
Yourself. :o

OK, just to clarify, we're also assuming that all three people in the truel actually want to win it.
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn

Online Dante

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Re: The Truel
« Reply #3 on: January 18, 2012, 01:33:47 PM »
Yourself. :o

OK, just to clarify, we're also assuming that all three people in the truel actually want to win it.

Meh, I figured with a 66% chance of missing, why not?  :laugh:

Edit: Then hopefully Goode kills Best, and if not, Best should kill Goode, then I still have a 50% shot at surviving.

And you thought I was joking.
« Last Edit: January 18, 2012, 01:35:46 PM by Dante »
Actually it doesn't. One could conceivably be all-powerful but not exceptionally intelligent.

Offline One Above All

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Re: The Truel
« Reply #4 on: January 18, 2012, 01:33:55 PM »
Yourself. :o

OK, just to clarify, we're also assuming that all three people in the truel actually want to win it.

1/3 chance that you'll hit yourself; 2/3 chance that you'll hit someone else.
Seems OK to me.
The truth is absolute. Life forms are specks of specks (...) of specks of dust in the universe.
Why settle for normal, when you can be so much more? Why settle for something, when you can have everything?
We choose our own gods.

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Offline pianodwarf

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Re: The Truel
« Reply #5 on: January 18, 2012, 01:36:02 PM »
Yourself. :o

OK, just to clarify, we're also assuming that all three people in the truel actually want to win it.

1/3 chance that you'll hit yourself; 2/3 chance that you'll hit someone else.
Seems OK to me.

I would think it was clear that the odds of hitting a target apply to aiming at a target, not aiming at yourself.  It's exceptionally rare for people who try to shoot themselves to miss, even if they have no experience with firearms.

Come on, guys... sheesh.
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn

Offline One Above All

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Re: The Truel
« Reply #6 on: January 18, 2012, 01:39:17 PM »
Come on, guys... sheesh.

It's a riddle. Usually these things have ridiculous solutions.
The truth is absolute. Life forms are specks of specks (...) of specks of dust in the universe.
Why settle for normal, when you can be so much more? Why settle for something, when you can have everything?
We choose our own gods.

A.K.A.: Blaziken_rjcf/Lucifer/All In One.

Online Dante

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Re: The Truel
« Reply #7 on: January 18, 2012, 01:42:09 PM »
Well, if I shoot at Goode and kill him, then I'm screwed.

If I shoot at Best and kill him, I've a 33% chance of surviving. If I shoot at Best and miss, and Goode shoots at Best and misses, I've got a 50% chance.

If I shoot at Best and miss, and Goode shoots at Best and hits, I've got better than 50% chance. So, I guess I shoot at Best.
 
Actually it doesn't. One could conceivably be all-powerful but not exceptionally intelligent.

Offline One Above All

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Re: The Truel
« Reply #8 on: January 18, 2012, 01:43:16 PM »
Forgot my answer:
Aim at something else that won't kill either one. The 66% guy will try to hit the 100% guy, since he's next and will most likely do the same, and there's only a 33% chance that he'll miss. Then, when it's your turn, aim at the 100% guy('s dead body) and there's a 66% chance that you'll hit the 66% guy.
The truth is absolute. Life forms are specks of specks (...) of specks of dust in the universe.
Why settle for normal, when you can be so much more? Why settle for something, when you can have everything?
We choose our own gods.

A.K.A.: Blaziken_rjcf/Lucifer/All In One.

Offline pianodwarf

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Re: The Truel
« Reply #9 on: January 18, 2012, 01:46:14 PM »
Forgot my answer:
Aim at something else that won't kill either one. The 66% guy will try to hit the 100% guy, since he's next and will most likely do the same, and there's only a 33% chance that he'll miss. Then, when it's your turn, aim at the 100% guy('s dead body) and there's a 66% chance that you'll hit the 66% guy.

Not exactly correct, but close enough.  Yes, your first shot, you aim at the ground.  Then you wait until it's your turn again, and you aim at whichever one of them has survived (you don't continue trying to miss, you waste only your first shot).

Aiming at the dead guy's body does *not* give you a 66% chance of hitting the other guy who's left.  A miss is a miss.
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn

Offline One Above All

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Re: The Truel
« Reply #10 on: January 18, 2012, 01:49:26 PM »
Aiming at the dead guy's body does *not* give you a 66% chance of hitting the other guy who's left.  A miss is a miss.

Ah. I thought that it was a sort of "If you don't hit one guy, you'll hit the other one" type of thing.
The truth is absolute. Life forms are specks of specks (...) of specks of dust in the universe.
Why settle for normal, when you can be so much more? Why settle for something, when you can have everything?
We choose our own gods.

A.K.A.: Blaziken_rjcf/Lucifer/All In One.

Online Dante

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Re: The Truel
« Reply #11 on: January 18, 2012, 01:58:50 PM »
You are the worst marksman of the three, hitting your target only 33% of the time. 


Not exactly correct, but close enough.  Yes, your first shot, you aim at the ground.   

But if you aim at the ground, and hit it, you've wasted your 1 in 3 chance of hitting your target. ;)

edit to add: The point being that if, in reality, one truly is only 33% effective at hitting the target, missing on purpose does nothing to increase those odds. One would have to try to hit the Best shooter, and hope they miss.

edit part deaux: where's the lightbulb smiley? I get it.  :-[
« Last Edit: January 18, 2012, 02:21:30 PM by Dante »
Actually it doesn't. One could conceivably be all-powerful but not exceptionally intelligent.

Offline pianodwarf

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Re: The Truel
« Reply #12 on: January 18, 2012, 02:12:00 PM »
But if you aim at the ground, and hit it, you've wasted your 1 in 3 chance of hitting your target. ;)

Now let's see if you can win James Randi's challenge... can you divine where I'm thinking of aiming my next shot?   ;D
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn