28 replies to this topic

[araver]

Spoiler for answer

assuming the two infected ones know who the other is you could gas all exept one. tell them to give give evryone syrum from their own rooms without even scaning them (make sure they do not touch anyone) then once they are back in their room gas them and have another person do the same. then just to make sure you didnt pick the two infected ones have a third person go and do it so no matter what one uninfected trustworthy person will have uninfected evryone
NOTE:tell evryone they are the first to be woken up and that no one has been injected yet

please comment and tell me if i missed anything

Comments:

Spoiler for

I like the bit about lying them about who is the first to be woken up / no one has been injected yet.

The flaw in your strategy is that you cannot make sure they do not touch anyone. All you have is a lousy video connection and no ability to see 360 degrees. So if the first one is infected, he may give the right serum + infect them at the same time without you knowing for sure. Which means the second and third person waking up would also be infected / infect the others also.

And I did not get the part with the two infected ones knowing which is the other infected one ... where does that come into play?

[Akariass]

Spoiler for Let's see...

I'm doing this as I type, so bear with me.
Gas 2 rooms and connect each one to another room, having the conscious one scan and cure if infected. This leaves a few possible scenarios:
1. both gassed rooms had infected people, so the base is cured.
2. one gassed room had an infected person and the other one went into his room
3. one gas room had an infected, and the other one went into the other gassed room
4. one gas room had an infected, and the other one was the last room
5. one conscious room had an infected, and the other one was in the last room

These situations end with the following possibilities:
1. all clear
2&3. 2 infected through one connected hallway
4. one infected
5. 3 infected, 2 connected and one separate from the others

In all cases there is at least one person who is not infected. Have the conscious people return to their original rooms and have the last person enter one of the gassed rooms and scan.
Thus, we can get the following situations:
1. all clear
2&3a. goes into the infected room; clears it
2&3b. goes into the clean room
4. infects the room he enters
5a. goes into the infected room
5b. goes into the clean room; infects it

With the following endings:
1. clear
2a. 1 infected
2b. 2 infected
3. 2 infected
4a. 3 infected
4b. 4 infected

I just noted that whatever happens, an infected person will always say that another is clean.
Also, in doing this I realize that assigning numbers to the rooms would have made the process of describing this much easier, so I will start this now: Starting from the isolated person and going clockwise around the (what I assume) pentagonal figure, it's 1-5. Thus, in the first step, 5 went to 2 and 4 went to 3, and 2 and 3 were gassed. Hopefully you can still follow what I'm saying.

Now have 1 return to his room, and once again have 5 scan 2. Depending on what he says, you can determine what situation we have (I hope)
If he says "clean," then it's either an infected person lying, or a clean person telling the truth. With a diagram (such as the one I drew that I have no idea how to put in here) one can see that it must be situation 1, 2a, 2b, or 4a.
If he says "infected," then it's a clean person telling the truth, and it's 3 or 4b. If that's the case, then you can just gas all the other rooms and have him go around cleaning everyone else.

Thus we're left with the former problem. Hm... Have 1 once again sweep, this time 2 AND 3, and if one of them is reported as "infected," then he's clean and have him clean the station as before. If he reports all clean, then you know that room 4 is the only clean one, and he can clean the rest of the station.

Now, I know that this solution can undoubtedly be cleaned up, as I didn't incorporate my assumption with the infected people until halfway through, and I also realize that that assumption may be wrong, although currently I can't think of a reason why that might be so.

[Assassinator]

Spoiler for Can you not

Note: if i say 1st i mean the first man sent in at the beginning here 2nd is second guy etc
Pick any random room and gas it, and then send 1 person from a different room to check the guy in it but do nothing regardless, then another guy to do the same (from a different room) and then another guy again to do it, but each time having only the gassed guy and the one there to check it in there at once. After this do it again, in reverse order. So the guy you sent in last go in again, then the 2nd guy, then the first guy.
After this you will have either
1 All clean - therefore they are all clean as only 2 people are infected and the infected ones cant have infected anyone else other than the gassed one and since you checked in reverse order if the infected guy was the first one then the other not infecteds would have seen infection if 2nd guy then first guy and 3rd guy would have seen it, it 3rd guy then 2nd and 1st would have. therefore one clean person would see it. Then gas all other rooms and send one of these guys to cure them.
2 one person says Infected at any point, then that guy is clean and gas everywhere else and have him check/cure them.
Then the base is cleared.
I have based this on that no infected person would say infected regardless of the actual result of the scan, and that any infected person would take an opportunity to infect an unconscious guy - otherwise this doesnt work.

[bushindo]

Some clarification please:

1) The OP indicates that video and audio communication are available between you and all areas. That seems to imply that you can simply pose questions to the crew members and have them respond. Does that mean that the non-infected crew members will act as truth tellers? Would the infected members then act as random answerers?

2) Suppose that a crew member is infected, and then is cured by a serum. Would he know that he was infected last round?

Edited by bushindo, 20 December 2010 - 04:59 AM.

[araver]

Some clarification please:

1) The OP indicates that video and audio communication are available between you and all areas. That seems to imply that you can simply pose questions to the crew members and have them respond. Does that mean that the non-infected crew members will act as truth tellers? Would the infected members then act as random answerers?

2) Suppose that a crew member is infected, and then is cured by a serum. Would he know that he was infected last round?

1) Yes
- Non-infected crew members act as truth-tellers.
- Infected members don't act random, they choose their responses adaptively to suit their interest (i.e. may try to act as truth-tellers - stick with their lies)
And a bonus clarification: they don't really know which of them is infected.

2) No. Infection may work as temporary subtle mind-control.

[araver]

Spoiler for Can you not

Note: if i say 1st i mean the first man sent in at the beginning here 2nd is second guy etc
Pick any random room and gas it, and then send 1 person from a different room to check the guy in it but do nothing regardless, then another guy to do the same (from a different room) and then another guy again to do it, but each time having only the gassed guy and the one there to check it in there at once. After this do it again, in reverse order. So the guy you sent in last go in again, then the 2nd guy, then the first guy.
After this you will have either
1 All clean - therefore they are all clean as only 2 people are infected and the infected ones cant have infected anyone else other than the gassed one and since you checked in reverse order if the infected guy was the first one then the other not infecteds would have seen infection if 2nd guy then first guy and 3rd guy would have seen it, it 3rd guy then 2nd and 1st would have. therefore one clean person would see it. Then gas all other rooms and send one of these guys to cure them.
2 one person says Infected at any point, then that guy is clean and gas everywhere else and have him check/cure them.
Then the base is cleared.
I have based this on that no infected person would say infected regardless of the actual result of the scan, and that any infected person would take an opportunity to infect an unconscious guy - otherwise this doesnt work.

A clarification: an infected person can scan and report whatever suits him best (i.e. he can either lie or tell the truth).
But an infected person indeed jumps on the opportunity to infect an unconscious person (this is their only deterministic flaw).

Comments:

Spoiler for

The steps in your strategy are like this:

2 checks/scans 1 
3 checks 1
4 checks 1
4 checks 1
3 checks 1
2 checks 1

Assume 2 and 1 are infected, 3 and 4 are clean. You get the following responses:

2 checks 1 says "Infected" (Truth)
3 checks 1 says "Infected" (Truth)
4 checks 1 says "Infected" (Truth)
4 checks 1 says "Infected" (Truth)
3 checks 1 says "Infected" (Truth)
2 checks 1 says "Infected" (Truth)

Assume 2 is infected, 1, 3 and 4 are clean at the beginning.

2 checks 1 says "Infected" (Lie, but gets to infect)
3 checks 1 says "Infected" (Truth)
4 checks 1 says "Infected" (Truth)
4 checks 1 says "Infected" (Truth)
3 checks 1 says "Infected" (Truth)
2 checks 1 says "Infected" (Truth)

That kills the "one person says Infected at any point, then that guy is clean" hypothesis, don't you think?

[araver]

Spoiler for Let's see...

I'm doing this as I type, so bear with me.
Gas 2 rooms and connect each one to another room, having the conscious one scan and cure if infected. This leaves a few possible scenarios:
1. both gassed rooms had infected people, so the base is cured.
2. one gassed room had an infected person and the other one went into his room
3. one gas room had an infected, and the other one went into the other gassed room
4. one gas room had an infected, and the other one was the last room
5. one conscious room had an infected, and the other one was in the last room

These situations end with the following possibilities:
1. all clear
2&3. 2 infected through one connected hallway
4. one infected
5. 3 infected, 2 connected and one separate from the others

In all cases there is at least one person who is not infected. Have the conscious people return to their original rooms and have the last person enter one of the gassed rooms and scan.
Thus, we can get the following situations:
1. all clear
2&3a. goes into the infected room; clears it
2&3b. goes into the clean room
4. infects the room he enters
5a. goes into the infected room
5b. goes into the clean room; infects it

With the following endings:
1. clear
2a. 1 infected
2b. 2 infected
3. 2 infected
4a. 3 infected
4b. 4 infected

I just noted that whatever happens, an infected person will always say that another is clean.
Also, in doing this I realize that assigning numbers to the rooms would have made the process of describing this much easier, so I will start this now: Starting from the isolated person and going clockwise around the (what I assume) pentagonal figure, it's 1-5. Thus, in the first step, 5 went to 2 and 4 went to 3, and 2 and 3 were gassed. Hopefully you can still follow what I'm saying.

Now have 1 return to his room, and once again have 5 scan 2. Depending on what he says, you can determine what situation we have (I hope)
If he says "clean," then it's either an infected person lying, or a clean person telling the truth. With a diagram (such as the one I drew that I have no idea how to put in here) one can see that it must be situation 1, 2a, 2b, or 4a.
If he says "infected," then it's a clean person telling the truth, and it's 3 or 4b. If that's the case, then you can just gas all the other rooms and have him go around cleaning everyone else.

Thus we're left with the former problem. Hm... Have 1 once again sweep, this time 2 AND 3, and if one of them is reported as "infected," then he's clean and have him clean the station as before. If he reports all clean, then you know that room 4 is the only clean one, and he can clean the rest of the station.

Now, I know that this solution can undoubtedly be cleaned up, as I didn't incorporate my assumption with the infected people until halfway through, and I also realize that that assumption may be wrong, although currently I can't think of a reason why that might be so.

Clarification: An infected person will not always say that another is clean. Each infected person acts as an independent agent of infection. You must not assume he has a greedy strategy that always protects the others he infects (he might sacrifice one and say they're infected when they are infected) and he can also choose to frame someone who is not infected or not to frame him in order to alleviate suspicions on him.

Spoiler for Comments on the proposed solution

You are partially right, it's harder to read in the beginning
You are right about the five scenarios that arise from 2 disjoint pairs of conscious/inconscious scan+disinfect. However, I don't really follow what happens after you put "the last person enter one of the gassed rooms and scan". Which room in your 1,2,3,4,5 rotation? Can you elaborate(taking into account the clarification above)?

[araver]

To make your strategies easier to explain you can use the following base diagram:


Alternatively, if you want a neutral / central location, you can assume one as well

Spoiler for

[Verrk]

Spoiler for Possible solution?

I believe sending 2, 3, 4, and 5 to scan an unconscious 1 separately and in order will eventually result in an infection of 1, and if everyone says he checks out clean you can assume 4 and 5 to be infected(along with 1, now) and you can send 2 and 3 to disperse the serum. in a more complicated scenario, say 5 says he's infected, but 5 is also infected and so giving him the serum will do nothing. then go back and have 4, 3, and 2 scan 1. if 4 was the other infected, 3 will confirm that 1 is infected. if 3 is the infected 2 will confirm, and if 5 and 1 were the original infected then 4's scan will say so. now, if they all say he's clean then 2 must also be infected as he would be the last one and could lie. then you could assume 3 and 4 are the two clean ones, and have them dispense the serum.

I am starting to second guess my solution now, as I am starting to see how:

Spoiler for Oh, crap.

an infected could lie saying one of them was infected when he wasn't and now there are 3 where you might have thought you found one.

I shall sleep on this one and return later.

[Jobe17]

Spoiler for

Without anyone contacting anyone else, send 4 of them one at a time to the door leading outside. There is a scanner connected to this door that will detect who is infected and who is clean. When a person reaches the scanner, it will set off an alarm if they are infected. Of the 4 people sent to the scanner, 1 or 2 will set off the alarm. Here are the possibilities for the two infected:

p1, p2 (2 doors)
p1, p3 (3 doors)
p1, p4 (4 doors)
p1, p5 (4 doors)
p2, p3 (3 doors)
p2, p4 (4 doors)
p2, p5 (4 doors)
p3, p4 (4 doors)
p3, p5 (4 doors)
p4, p5 (3 doors)

Once you have found out who the two infected individuals are, gas their rooms and send one of the non-infected persons to inject them with the serum from their own room.

Min doors opened: 4
Max doors opened: 6
Avg doors opened: 5.5
Risk of spreading infection: 0.0%