80 replies to this topic

[Malfure]

i would rather be a pacifist if there was an even or odd # of killers cause i would try to get out of the village

[ah2190]

Given the origanal situation, I would NOT want to be a killer. Because, killers would kill each other in pairs until there are no killers left. I would try and advoid them until they are all dead, which would mean I would survive.

However, in the situation of there being 11 killers, I would WANT to be a killer. This is because after 5 meetings that have both sides as killers, there would only be one killer left, and no-one that can kill that killer.

Therefore, if I was in Killville, I would want to be a Killer if there are an odd number of Killers, and not one if there are an even number of killers. And if I was to move in, I wouldn't move in while there are an odd number of killers at large.

[Thuhchris]

Hint 1: What does it mean to survive?

Hint 2: Would the result be different if Killville were populated by 11 killers and 11 pacifists?

Spoiler for #1

Someone up there ^ must like you.
Just kidding....idk

Spoiler for #2

Being a killer would have a better survival chance, because if a killer meets a killer then they both die. that means, in order to kill all the killers you need an even number

so basically if there is an even number of people, the pacifists would have a better chance
and if there is an odd number only one person (a killer) would survive

[Magic Leprechaun]

Spoiler for My long-winded answer and explaination

If you assume the meetings are random, i would like to be a pacifist. If it is random there should be an equal number of each of the following outcomes:

Killer vs Killer
Killer vs Pacifist
Pacifist vs Pacifist

so after one of each outcome the population would be 9 pacifists and 8 killers, (two killers meet, 2 killers die, two pacifists meat noone dies, killer meets pacifist one pacifist dies)

so by the time only half the pacifists have died, all the killers will be dead, meaning any pacifist will have a 50/50 chance of surviving, wilst the chances of a killer surviving is 0.

if there were an odd number of killers, then you should be a killer, because killers only die in pairs, so one will survive to kill all the pacifists

[giterdone]

The riddle has already been awnsered. Unless you have anything important or a different awnser that hasn't already been posted, then you shouldn't post awnsers in an old thread. I am quite sure that a mod will probally lock this topic soon because it is already done with.

[rpupkin77]

Simple answer is:

Spoiler for simple solution:

Assuming that meetings random and that to begin there are the same amount of each type then survival is essentially equal. Both groups have a 50% chance of interacting with the other kind and therefore both groups have a survival chance of 50% for each encounter.

However, I think the long term survival chances for every individual is 5%.

Killer populations will drop in spikes and the pacifist population will drop on a gradual slope.

Edited by rpupkin77, 16 June 2008 - 04:04 PM.

[wfwood]

Kudos to writersblock [2nd post basically does it]

Spoiler for solution

Only killers can kill killers, and they die doing it; so killers die in pairs.

Starting with 10 killers, all the killers will eventually die, two at a time.
[killer chance of survival = 0.]
[pacifist chance of survival depends on ability to hide until last killer is dead; risky proposition, but not 0.]
So you want to be a pacifist.

Starting with 11 killers, eventually 10 killers will annihilate themselves pairwise, and the surviving 11th will eventually kill all the pacifists.
[killer chance of survival = 1/11]
[pacifist chance of survival = 0.]
So you want to be a killer.

But do all the pacifists go first? If all the pacifists go first then nobody survives. You have an overall chance of surviving longer if you are a killer. So basically there is a possible outcome where there are no survivors if we are talking about the long run here.

[Lemeshianos]

You live in Killville - a town populated by 10 killers and 10 pacifists.

When a pacifist meets a pacifist, nothing happens.
When a pacifist meets a killer, the pacifist is killed.
When two killers meet, both die.

Assume meetings always occur between exactly two persons
and the pairs involved are completely random.

Are your odds of survival better if you are a killer? or a pacifist?
Or does it matter?

Spoiler for hint

Regardless of whether you are a pacifist or a killer,
you may disregard all events in which a pacifist other than yourself is involved
and consider only events in which you are killed
or a pair of killers other than yourself is killed.

Actually I think the solution is simple. Don't have to take in account probabilities and math.
When you have an odd number of people in each group, after all meetings take place, a killer will be left standing. That means if you are a killer, you have a chance of never meeting with another killer and staying alive.
In the case of an even number of people in each group, it is certain that at some point, all killers will meet each other. The "game" doesn't stop when all pacifists die. So if you are a killer it is certain that you will die, while being a pacifist you have chances of surviving if all killers die before you meet any.

[Sir Viss]

So I know this is an old topic, and I don't know if anyone will read this, but I found this site today through iGoogle, and found this puzzle.

After generating a formula for deriving possibilities and adding them up, and comparing vectors and on and on, and generally overworking excel, I went to total the odds of being the sole surviving Killer, and realized, there was no column in my table for that, and of couse then it hit me that there wasn't going to be one.

Then I came and read all the posts, and investigated myself, and the formula that the odds of surviving as a pacifist in an even Killer scenario are in fact 1 / (K+1) where K is the number of killers. This can actually be demonstrated through induction, but I'll save it.

I posed the question to a friend, and he asked if I meant that he was one of the 20, or if he was moving into town and had to choose a team, because in that instance, he found it strange, his odds were even no matter which he picks!

So the coolest result of all, is that if you have to pick a behavior pattern to adopt, then knowing the number of total residents, and the make-up of the Killer to Pacifist balance are totally irrelevant. Beyond that, you can't affect your odds by choosing either lifestyle. If the number of existing Killers is even, then you get your 1 / (K+1) shot either way, and if the number is odd, you're doomed no matter which way you go.

Cool.

Great site, btw for anyone who is listening.

[Chuck Rampart]

So the coolest result of all, is that if you have to pick a behavior pattern to adopt, then knowing the number of total residents, and the make-up of the Killer to Pacifist balance are totally irrelevant. Beyond that, you can't affect your odds by choosing either lifestyle. If the number of existing Killers is even, then you get your 1 / (K+1) shot either way, and if the number is odd, you're doomed no matter which way you go.

That is a very cool result. I spent a long time trying to prove you wrong, but I've convinced myself you are right.