Satisfied, Princess Celestia nods her head. The question she was looking for was one where you trusted another friend to come to the answer to her puzzle: trust is key.
She leads the three of you back to the throne room to announce that you have passed, to the relief of the remaining ponies. She then explains what is going on.
Recently, Canterlot has received an unprecedented number of foreigners directly from the Gazelle Plains, which was apparently in response to a deadly disease that had gripped the land - a terrible virus known as Geo-orgosis. Sufferers of the disease show no external symptoms until a few moments before their body suddenly crystallizes into a solid mass resembling hard diamond, and the only way they know they have the virus is a very strange feeling inside...
It is believed that the gazelles carrying the virus were exiled from their home and quarantined in Canterlot - without permission from Celestia or Luna. And since Canterlot isn't really prepared for such a sudden population increase nor the sheer paperwork necessary to try and either send them back or keep them, they are sending the seven of you directly to the Gazelle Plains to try and ascertain the situation and resolve it. She adds that she has faith in Twilight's anti-biohazard spell and recommends casting it on you all before you leave.
You then catch the next airship to the Gazelle Plains (and this time Rainbow Dash doesn't need to queue up behind 499 other ponies to get on) and you are whisked away to the lands directly neighbouring Zecora's Zebra Lands...
Upon your arrival, all seems perfectly normal. Twilight then recommends that everypony try and get a feel of the place before trying to speak with the higher ups - but as she does, she sees a nearby male gazelle unfortunately increase his own bodily density by several times by inconveniently crystallizing himself. Twilight only manages to freeze the process enough to allow his face to remain intact, where he admits a shocking truth: there are many more gazelles with the disease, but aren't coming forward out of fear of spending their final few weeks in exile. Unfortunately, that is all he can manage before the spell breaks and he becomes a rather handsome garden ornament.
Realising that this needs to be taken up with the rulers of the Plains, they quickly borrow several tourist maps and frantically make their way towards the Plain Palace (which, as they discover, certainly is an appropriate name, in more ways than one: it's a solid grey). They quickly barge into the palace and demand to see whoever's in charge. It takes Twilight Sparkle flashing some sort of very shiny badge and a lot of titles being thrown around on the part of Twilight before you're finally granted an audience.
You are then taken to the Supreme Leader: a gazelle wearing rather thorny and rather dangerous attire, including a literal crown of thorns, causing Rarity to wonder how it doesn't just catch in the fur or mane, where Twilight explains Canterlot's sudden population increase.
The Supreme Leader concedes that it was unfortunate on the part of the ponies, but he was left with no recourse: it was the only way to contain the outbreak of Geo-orgosis. And it evidently worked: since then, the number of gazelles admitting they had the virus dropped to precisely zero. Applejack then points out the gazelle they saw that got the authentic cockatrice experience, but he laughs it off, and Pinkie and Rarity have to restrain Rainbow Dash from punching him in the face and/or yelling at him.
Twilight asks if they are at least working on a cure, but the Supreme Leader doesn't see the need for it, given how the problem was 'solved'. But he does concede he could be wrong and that it's worse than he thought - but only if you can prove it. Only if the seven of you can prove the disease is still rampant will he and his best doctors sink the money into a cure. However, suspicious of how the ponies have a vested interest in ridding themselves of any illegal immigrants, he says that he will not accept any secret ballots, or anything that doesn't provide the names of the surveyed gazelles along with their entries/answers. Furthermore, he must be able to contact every gazelle to confirm they answered exactly as recorded, to avoid any falsehoods and fake news.
After finding themselves outside the palace, the seven of you try to brainstorm some ideas. Fluttershy is certain everyone who has Geo-orgosis knows that they have it, and Applejack is certain that they would all understand the importance of the survey and tell the truth. However, it is pointed out by Pinkie that no-one is willing to own up to having Geo-orgosis or else they get a one-way trip to Canterlot, and starts trying to devise some sort of secret code, but Rarity reminds everypony that codes can't be allowed - the Supreme Leader's government said no secret answers.
Everypony seems completely stuck for ideas, until the six of them turn their heads to you for YOUR opinion. They are all clearly in a quandary. How CAN the seven of you survey the population, accurately establish the spread of Geo-orgosis, and get all who have the disease to admit to it, while making sure no-one can ever use the information against them?
It's up to you to take everything you learned so far and try to find the answer and make sure the entire Gazelle Plains doesn't becomes populated with lumps of biological rock!
This is your toughest riddle.
Couldn't they just drag in the guy they saw get crystallized on the way there?
9265632
Dude c'mon. What if he has a family?
Couldn't we just ask everyone and then say X%of the population is sick?
9265899
Wait, can we ask everyone if they know somebody with the illness? Because by the logic of rule 1, it seems to say everyone without the illness knows they aren't sick
9266015
Too ambiguous. What if we have a group of ten friends with only one infected? At least nine will say yes, which skews results dramatically. Or ten, if the infected pony decides to refer to themselves, and with no way to tell you're stuck.
9265824
Bring them, too, so they can back up the heroes that this guy totally just turned to crystal and there's still a problem.
Ask the gazelles "Do you know anyone afflicted with the illness?"
If yes, which will be a lot of the population, then it's proven that the disease is still rampant, especially since the gazelles are telling the truth.
The benefit of this question is that public ballots can be given and all answers can be corroborated without issue.
9266139
Duck gave a similar answer. See my rebuttal below
9266214
And? No-one is owning up to having it. It's not a secret code. It's perfectly public "Do you know someone afflicted." Nothing can trace that back to the afflicted ones.
9266216
Nor does it accurately establish how far Geo-orgosis has spread, which is one of the conditions of the puzzle.
Here's my attempt.
Everyone will take a three-part survey, answering in each part "Do you have Geo-orgosis?" However, they are instructed to randomly select one part to answer falsely (so someone with Geo-orgosis may answer "Yes, Yes, No" or "Yes, No, Yes" or "No, Yes, Yes" while someone without Geo-orgosis may answer "No, No, Yes" or "No, Yes, No" or "Yes, No, No"). Then, after all of the surveys are collected, two of the three parts of each survey will be destroyed, and the remaining part will be reported (the same part for each survey, decided beforehand and kept secret from those surveyed, so that there won't be any claims of bias).
The key point about this survey is that whether someone has Geo-orgosis or not, they will give the following three answers: one "Yes" answer, one "No" answer, and one true answer. One of the three will be selected at random to report, so we should expect to get 1/3 "Yes" answers and 1/3 "No" answers, leaving the remaining 1/3 as true answers. So when interpreting the results of the survey, for example, if we have 3000 responding and we get something like 1300 "Yes" and 1700 "No", we would ignore 1000 "Yes" and 1000 "No" answers, leaving 300 "Yes" and 700 "No" answers, meaning Geo-orgosis is in about 30% of the population.
The one sticking point is how much information is given about individuals. Certainly, someone who gave a "Yes" answer is more likely to have Geo-orgosis than someone who gave a "No" answer, but it's never a sure thing, because the answer could easily be one of the false ones - and since the other parts were destroyed, there's no way to tell for sure if any individual answer is true or false. I'm not sure if the increased likelihood for the "Yes" answers is too much.
9266290
What do you mean by "Everyone will take a three-part survey, answering in each part "Do you have Geo-orgosis?"" Does that mean they answer the same question three times, or they lie about a third of the question, or they get asked three questions, including "Do you have Geo-orgosis?"
9266346
I believe it's the same question thrice.
9266458
Well then it's one lie against two true answers, so the majority answer is the true one, and thus can be traced back to an individual having Geo-orgosis. So it wouldn't work.
9266485
But one answer is destroyed.
9266489
Well it still creates problems. When an individual would get surveyed this way, one of four results occurs (assuming results are destroyed randomly):
Eliminate two yes's, leaving a single no.
Eliminate one yes and one no, leaving a single no.
Eliminate one yes and one no, leaving a single yes.
Eliminate two no's, leaving a single yes.
You would be destroying the majority answer, assumed to be the truth if you only get to lie once, 50% of the time, which skews the results of your survey. And remember, the government MUST be able to confirm that each individual answered exactly as recorded in the survey: if a majority answer is yes, and the official report submitted says no, we have a problem should the government contact them. A falsehood means they will not accept the result.
Get 100 survey takers.
Line them up in a 10 by 10 square.
We'll ask them 2 questions.
1.Do you have Geo-orgosis?
2.How many next to you have Geo-orgosis?
That means the one to your left, your right, in front, and behind you. Do not count yourself.
The first one we keep to ourselves.
The second one is the one we report in.
If 35 said yes to the first one, we report that 35 out of 100 will turn into a crystal.
If we need a bigger sample size, we make the square/rectangle bigger.
A less complicated, but more math heavy method.
Ask them what percentage of the town will turn stiff.
You'll have a lot of guesses, but you can average out a pretty accurate answer.
9267402
What, you'd turn the entire Kingdom into one big Minesweeper game, except with names recorded? That can be traced using logic.
Your survey must contain NO info as to whether or not an individual has Geo-orgosis.
9266557
First, the "skewing" (putting aside the fact that the four results you listed are not all equally likely) is already taken into account by my method. Here's my chain of logic, so that if I'm wrong you can point out where.
Everyone submits among their three answers either "Yes, Yes, No" or "Yes, No, No" in some order.
Therefore, everyone's answers can be rearranged into "Yes, (the true answer), No" regardless of whether they have Geo-orgosis or not.
When two of these three answers are destroyed, the one reported is completely random among these three.
Therefore, we expect to get 1/3 "Yes" answers, 1/3 "No" answers, and 1/3 true answers (whatever they may be), so while there is technically some skewing, it is predictable.
To interpret the answer, we "un-skew" it. I provided an example in my initial post: if we have 3000 replies and they are 1300 "Yes" and 1700 "No", then since we expected to get 1000 "Yes", 1000 "No", and 1000 true answers, we subtract the 1000 from the "Yes" and "No" tallies to get our true approximation, 300/700 - a 30% infection rate.
Of course, the government will still have all 3000 replies available to check, and they'll know about the mechanics of the survey so they'll understand how the results are being interpreted.
Second, I'm not sure I understand your statement about discrepancies. All the government has is one of the three parts, so that's all they can check. "What was your majority answer?" "It was No, but part B was reported, wasn't it? That was the part I chose to lie on, so that part is Yes." "...Well, your part B does say Yes..." I'm not sure what the issue is.
9267758
So they clarify the true answer, which in turn links that individual as to whether or not they have Geo-orgosis? That defeats the point of the puzzle.
9267792
I'm sorry, my example was unclear. Let me give another example, one that is completely possible under my system. "What was your majority answer?" "No." "Well, that checks out, the answer you gave to part B was No." "That's certainly true." *thinks: But I don't want you to know that I put Yes down on parts A and C. Good thing those were destroyed so you have no way to check it!*
9267800
Okay? And what about all the other ponies unfortunate enough to NOT have their true 'yes' answer destroyed and thus as far as that government knows has Geo-orgosis and is getting deported to Canterlot? When I say no-one must be linked to having Geo-orgosis, I mean NO-ONE.
9267810
And how is the government supposed to tell which of those "Yes" answers were true ones and which ones were false ones? Is your claim that the government will naively banish everyone with a "Yes" answer, while being fully aware that a good portion of them are false positives and that there will be a good portion of false negatives that will be missed? If that's the requirement of the puzzle - to put it explicitly, everyone must have an EXACTLY equal chance in the government's eyes of having Geo-orgosis, regardless of their individual responses to the survey - then I will concede the point and go back to the drawing board.
9268319
There's also the fact that you're basically proposing that in the event of their submitted answer being no when the majority answer was actually yes, they lie. So if everyone is given license to lie, then since no-one is going to admit to having Geo-orgosis it means EVERYONE will answer no regardless of whether it was true or not, and your survey would lose its point.
The puzzles requirements are:
1. You must conduct an accurate survey of the gazelle population.
2. Everyone wants the true infection rate to be established accurately.
3. However, no-one will do anything that would leave them on record as having Geo-orgosis out of fear of banishment.
4. The government insists that the actual answer given by everyone surveyed is recorded alongside their names to avoid fraudulent answers.
9268620
See, I'm still not sure I completely understand your objection. Is there some misunderstanding of the survey itself? No one decides which of their own three answers will be reported - that was decided beforehand, and is kept secret until the survey is complete. So there's no way for someone to decide "My submitted answer will be a No." The only way to guarantee a "No" result is to have all three answers to the survey be "No," and it's easy to check each survey after it's filled out just to make sure the answers are not all the same. And if you're worried about us looking at the surveys after they are filled out but before the other parts are destroyed, that can be solved relatively easy, but I doubt that's the problem. If you're then going to claim that someone with Geo-orgosis will still pretend to not have it and play the odds by giving two "No" answers and one "Yes" answer, then we're back to the whole probabilities vs. certainties thing I went over before, since that would not eliminate the possibility that "Yes" is submitted anyway.
Having said all that (and I do not believe I need to spoil this part), I concede that if the requirement is what I said in my previous post, that the odds of someone having Geo-orgosis be EXACTLY the same regardless of their answer, then my solution does not meet that requirement. I suppose that is the major question I have: is how I'm stating the requirement there the way that you intend it? No further justification of WHY that is a requirement is necessary, just that it is the intended interpretation.
9269187
Well then short answer, no.
My problem is not that they don't get to decide the submitted answer: it's that you're giving them permission to lie as necessary, which defeats the point. Even if they don't lie in the survey itself, you gave them permission to lie to the government about whatever answer made it to them.
If you want the government to accept this as reliable results, there must be no lies.
9269557
I think I see where the confusion might have come from given the example situations I used, but quite frankly, your statement that they have permission to lie about the answer that made it to the government is false. If you look back, you'll see that in each example, the answer that made it to the government was confirmed to be the answer submitted for that particular part. Perhaps I got stuck on having the government ask about any given person's majority answer, since that's where the language at the time was leading. This would be more accurate: "The results we got were of part B, and you answered Yes to that part. Is this true?" "Well, yes, it is. That means that either I have Geo-orgosis and chose either part A or part C as my false answer, or I don't have Geo-orgosis and chose part B as my false answer, and you have no way of confirming which possibility is the real one. Is there a problem with that?" And the only way there is a problem with that is if probabilities matter instead of just certainties.
9269905
Government stipulation says the answer CANNOT be kept a secret.
Really should have just said that from the start I guess.
9270331
And what is kept a secret? The reported answer? It's literally what is provided to the government. The majority answer? There isn't a slip of paper on it anywhere that says "This is the majority answer," it's only something that can be inferred from the three answers, so that can't be the root of the issue. The only way what you've stated makes any sense is if the problem is with the destroyed answers, but those are not used in any way to calculate the reported percentage. If your insistence is that no collected information - even information that goes completely unused in the calculations - can be destroyed, then I guess that's that.
Incidentally, I had recently thought of a possible alternative, a sort of two-stage process where in stage one everyone answers honestly, then in stage two everyone randomly draws one of the stage-one answers from the pile, destroys it, and reports whether it was a Yes or a No, but that wouldn't satisfy your conditions either since the stage-one answers get destroyed.
9270404
...wait. In your scenario, is the government aware of how you're conducting the survey?
9270404
"This would be more accurate: "The results we got were of part B, and you answered Yes to that part. Is this true?" "Well, yes, it is. That means that either I have Geo-orgosis and chose either part A or part C as my false answer, or I don't have Geo-orgosis and chose part B as my false answer, and you have no way of confirming which possibility is the real one. Is there a problem with that?""
Yes. No trustworthy results means no action on the government's part.
9270579
Yes, the government is fully aware of how I am conducting the survey. I feel like it would be against the spirit (if not the letter) of the puzzle to directly mislead the government in the mechanics of the method. This is particularly true when the method involves individual responses that are sometimes false by design. Plus, with the way the results need to be interpreted, the government needs to be aware of the mechanics of the survey in order for it to work properly.
Also, I explained in my initial post how the reported answers, though any individual one might not be trustworthy, can be shown to collectively behave in a predictable way that can lead to a reasonably accurate estimate of the spread of Geo-orgosis. I'll go ahead and restate them here, hopefully more clearly: everyone submits three answers. For those with Geo-orgosis there are 2 Yes and 1 No (let's call them "Yes A," Yes B," and "No A"), and for those without Geo-orgosis there are 2 No and 1 Yes (let's call them "No A," "No B," and "Yes A"). Either way, anyone taking the survey has a 1 in 3 chance of submitting "Yes A," a 1 in 3 chance of submitting "No A," and a 1 in 3 chance of submitting either "Yes B" or "No B," depending on if they have Geo-orgosis or not - and note here that these Yes B and No B answers are true ones. In other words, we expect 1/3 of the responses to be "Yes A" which may or may not be true, 1/3 of the responses to be "No A" which may or may not be true, and 1/3 of the responses to be either "Yes B" or "No B" which are guaranteed to be true - and since it's completely random which ones they are, the percentage of these B responses that are Yes should be approximately the percentage of cases of Geo-orgosis.
Now, say we take all of the reported answers and arrange them in a line, with all of the "Yes A" results on the left, followed by the "Yes B" results, then the "No B" results, then the "No A" results. Based on the expectations above, the left 1/3 of the line is taken up by the "Yes A" results and the right 1/3 of the line is taken up by the "No A" results. This means the middle 1/3 contains the B results, and so the middle 1/3 is what needs to be examined. Of course, in real life, since we can't tell the A results from the B results, the "Yes A" and "Yes B" results will get mixed up, as will the "No A" and "No B" results, but the dividing point between Yes and No is still the same, so what we have is completely indistinguishable from the situation I described. Therefore, we can use the same method (ignoring the left 1/3 and the right 1/3 and using the ratio of the middle 1/3 as our estimate), with the added benefit that there is no particular "Yes" that can be claimed to be "Yes B" and so be used to tie someone to Geo-orgosis.
Having said all this...
While I do still feel like I can make the case that my initial method does meet the requirements, I've thought more about that alternate method I mentioned in my previous post. I've come to the conclusion that it is better than my previous solution in at least three ways: the estimate is more accurate, the reported results have absolutely no bearing on whether or not any individual has Geo-orgosis (not even on the probabilities), and the method does not rely on any responses being false (I would argue that the only advantage this last one gives is that it makes the method easier to understand, but, well, an advantage is an advantage).
Here is the alternate method. There are two surveys conducted: Survey A, and Survey B. First, in Survey A, participants answer honestly if they have Geo-orgosis (one answer, no complicated multiple-answer things like before). After Survey A is complete, Survey B begins.
In Survey B, participants randomly draw one response from Survey A, answer honestly whether it was a "Yes" or "No" answer, and then burn the Survey A response. This way, the result of Survey B is to effectively erase all of the names off of Survey A and replace them with irrelevant names. Survey B is reported after it is complete. Of course, the government and all participants are fully aware of how these surveys work.
The participants of Survey A have no reason to lie, because they know that in the end their signatures will be effectively removed by Survey B, so the estimate from Survey A is accurate. The participants of Survey B have no reason to lie, because their answers have nothing to do with them. Even if someone took both surveys and wound up drawing their own response, no one else would know they drew their own name - after all, they don't report whose survey they drew - so they would still have no reason to lie. Therefore, the estimate from Survey B is the same as the estimate from Survey A, and as such is accurate.
Maybe... we should ask every gazelle: are the chances of your having the desease above 50%, or are they not? Then those, who know they are sick, will answer: above. For the king that'd mean, there is a possibility of that gazelle's being ill, but it'd be just a possibility .
Meanwhile those, who are not sick, will be unsure , but will try to answer honestly anyway. And they'll be glad to discover, that they are not .
Perhaps, it is a solution, don't you think, everypony ?
* Knowing, that we could overcome this catastrophe, fills us with determination !
9507820
The puzzle clearly states everypony with the disease KNOWS they have it. So this would never fly.