You live in Killville. Can you stay alive?

[bonanova]

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?

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.

[Guest]

Hmmm. This is an ambiguous question I think. I read it originally as surviving one encounter, but it can also be understood to be the "last man standing."

If it's last man standing, then the 11 and 11 becomes easy. If there are 11 killers, there will eventually be one K left with no other killers and he would therefore go on to meet and off all the pacifists. The 10 and 10 gets harder. There is a possibility that all of the pacifists will be dead before the last 2 killers meet, but all of the killers are guaranteed to meet eventually, meaning they are assured death. The pacifist could get lucky and not encounter a killer ever, depending on the timing of the meetings. This means with 10 and 10, the killer has a zero chance of survival, where the pacifist would have at worst a 1 in 6 shot of living. I figure this by assuming 9 p's are dead already. There are 10 K's and this 1 P. At most there can now be 6 meetings. If P shows up at meeting 1 -5 he's dead. If he shows up at meeting 6, it's just him ... all the K's are dead and he lives. (I know it's not really a meeting, but 5 other meetings of K's have taken place.)

[Guest]

You want to be a killer. The killer has a 3 in 4 shot of surviving an encounter where a pacifist only has 1 in 4 survival odds.

If you take any known person, P or K then the odds of the encounter are 50/50 or 1 in 2 that the other will be a P or K. However, if both are unknown, there are 4 states:

P meets K - P dies

K meets P - P dies

K meets K - Both K's die

P meets P - they go to the pub and raise a pint

Personally, I'd rather be a P, spread the rumor that there is a block party and wait for the K's to off each other before I ever come out of my house.

[Guest]

Not sure if this approach is correct

If we take two people randomly from the 20, we will have

P and P : with probability of (10/20)*(9/19)=0.237

P and K : with probability of (10/20)*(10/19)=0.263

K and P : with probability of (10/20)*(10/19)=0.263

K and K : with probability of (10/20)*(9/19)=0.237

P survives when we draw (P and P) + (K and K) : 0.236+0.236=0.472

K survives when we draw (P and P) + (K and P) + (P and K): 0.236+0.263+0.263=0.762

I will go for K -- better to stay one more day

[unreality]

killers have 1/19 better chance of survival

Basically, it's the odds of if you will meet a killer.

A pacifist could meet 10 killers or 9 pacifists

10/19

A killer could meet 9 killers or 10 pacifiests

9/19

[bonanova]

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?

[Guest]

since all 3 possible meetings [p-p, p-k, k-k] are equally likely to begin with, suppose after 3 such meetings each type has taken place. at that point there would be 2 dead killers and one dead pacifist leaving 8 k's and 9 p's. at this point, the odds change a little against the p's and each successive 3 random meetings would raise the likelyhood of p's loosing their lives but even at this rate, the killers would surely be gone before the last pacifist meets one... in fact, i think the odds are that there would be about 3 or 4 pacifists left after all the killers are all gone.

[Guest]

you could have equal chances no matter what, just get a bus

[bonanova]

Hint: the answer is different if there are 10 killers from the answer if there are 11 killers.

[bonanova]

Kudos to writersblock [2nd post basically does it]

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.

[Guest]

Based on boring recursive simple mathematics, I figured out the following:

1) If people only meet in pairs 1 time, you have a 50/50 chance to survive (10K, 8K2P, 6K4P, 4K6P, 2K8P, 10P)

2) If people meet over and over and over until people stop getting killed, you have 0 Killers. As a Pacifist, you have a 31.25% chance of survival... someone else want to double check the math for me? I did it quick, dirty, and am still human.

[bonanova]

I think this is the simplest analysis:

Killers eliminate themselves pairwise. So an even number of killers eventually eliminate themselves - you'd want to be a pacifist then.

An odd number of killers eventually become a single killer that eventually eliminates all the pacifists - you want to be a killer then.

[Guest]

You want to be a killer. The killer has a 3 in 4 shot of surviving an encounter where a pacifist only has 1 in 4 survival odds.

If you take any known person, P or K then the odds of the encounter are 50/50 or 1 in 2 that the other will be a P or K. However, if both are unknown, there are 4 states:

P meets K - P dies

K meets P - P dies

K meets K - Both K's die

P meets P - they go to the pub and raise a pint

Personally, I'd rather be a P, spread the rumor that there is a block party and wait for the K's to off each other before I ever come out of my house.

Wouldn't P meets K be the same as K meets P? One of them should be eliminated from the probability equation, making P the better choice.

P meets P - P population stays same

K meets K - K population minus 2

P meets K - P population minus 1

In one out of three meetings One P will die.

In one out of three meetings Two K will die.

[bonanova]

Wouldn't P meets K be the same as K meets P? One of them should be eliminated from the probability equation, making P the better choice.

P meets P - P population stays same

K meets K - K population minus 2

P meets K - P population minus 1

In one out of three meetings One P will die.

In one out of three meetings Two K will die.

Think what it means to survive.

It's more than just getting past the first encounter.

What happens when an indefinite amount of time has gone by?

[Guest]

Are your odds of survival better if you are a killer? or a pacifist?

** your only chance for survival is to be a pacifist and the even number of killers kill each other off first.

Situation I - When a pacifist meets a pacifist, nothing happens.

Situation II - When a pacifist meets a killer, the pacifist is killed.

Situation III - When two killers meet, both die.

As a Pacifist, your only chance of survival (over an infinite period) would be that 5 pairs of killers met before your ticket was punched.

As a Killer, you would have 9 other killers out there... best case would be that 4 pairs of killers meet but this would still leave one other killer (your nemisis) which you would eventually run into. (assuming there must be a meeting)

Edited February 13, 2008 by Bad Dog

[Guest]

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?

Reply --

1.) to survive means that you have no chance of being killed by a killer ... (assumed)

2.) result dif with 11 Killers and 11 Pacifists: Absolutely... odd number of killers would mean that one will always be around to kill and he would be the last man standing... so this would mean that it is better to be a killer and hope your the one that never meets another killer.

[Guest]

Going back to the original question, the odds of surviving while being a killer are 190/380, which when simplified is 1/2. the odds of surviving if you are a pacifist is 180/380, which simplifies to 9/19. i would much rather be a killer.

[Guest]

Seems even number of killers = death to all killers.

Therefore Ps survive

Meanwhile

http://www.secretnuclearbunker.com/index2.htm

There are road signs for this - and then you just have LOL

[Guest]

there is a 33% chance of the 3 things happening. if all three do happen this many times pacifists end up surviving.

[Guest]

it really depends in the order they met- should the killer always meet with a pathfir then everyone will die- if the pathfir should be the last people remaining then the killers met each outher first- it doesnt matter because yoiu dodnt no the sequence

[Guest]

What would be nice would be to turn the question into more of an anthropology compete/cooperate question. For example,

During a P/K confrontation, there is an 80% chance the Killer will survive and the Pacifist dies, 9% chance no outcome, 10% chance Pacifist kills Killer, 1% chance a P/K alliance forms, effectively creating a new entity that has different characteristics of interaction with other entities.

During a P/P confrontation, there is a 10% chance an alliance will form, effectively unifying the P/P pair into a new P with greater chances of survival in a P/K confrontation, 90% chance no outcome

During a K/K confrontation, there is a 50% chance one will die, a 40% chance no outcome, a 10% chance a K/K alliance forms, effectively making a new K with more successful victory chances in any confrontation

Also add that the chance of an encounter increases by some factor as population increases.

Let us also assume that confrontations are over resources, so we also add that at any encounter there is a probability P1 of a confrontation, which is variable depending on how each side perceives availability of resources. The larger the total population, the less available resources seem.

of some kind and as the population increases the chances of confrontation increase because of relative resource scarcity, conversely for population decreases.

Let's also throw in that all alliances have a inherent stability, where at each moment in time there is a probability of dissolution. P/P alliances are stronger than P/K alliances.

Let's also note that alliances can expand, eg: a P/P alliance meets a new P, thus forming a P/P/P alliance, with yet further enhanced characteristics.

Let's also add the rule that alliances can create technology, effectively increasing perceived availability of resources. Also, the rule that the longer an alliance is in existence the better technology it has. The technology is measured in an alliance as some recorded 'quantity', and the more of it the more the alliance perceives resources as available. Also, the more it has, the better chances it has of surviving a confrontation.

Now, what do you want to be? a P or a K?

Intuitively I'd guess that P-type alliances will triumph with oscillations in amount of K membership.

Edited March 6, 2008 by Oblivion

[Guest]

kk im going k.

p + p = 9/20 chances to live.

p + k = 10/20

9-10=-1 lifes

k+p= 10/20 live

k+k= 9/20 deaths

10-9= +1 lives

Kiger

Edited March 8, 2008 by kiger

[Guest]

I personally thought what no one else thought why dont whoever wants to stay alive leave? it is so much more sensible then they could go to liike peaceville and btw this isn't a joke

[Guest]

Truthfully it really doesnt matter because no matter if you are a pacifist or a killer you die. My advice get out of Killville.

[Guest]

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?

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.

pacifist because killer+killer=2 died population down pacifist+killer=1 died poulation down by 1 pacifist+pacifist=no one dies

answer=PACIFIST

[Guest]

bona - your puzzles are usually so well written and easy to interpret. This one was slightly ambiguous which threw me off. Regardless, I liked it a lot.