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// The Answer 39 
// Story: Life is a Test: A Series of Pony Logic Puzzles 
// by Brony_of_Brody 
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The first thing that should become obvious is that there generally won't be a single question that will satisfy the criteria of an accurate survey, non-anonymously carried out, that gets a gazelle to confess they have Geo-orgosis, while also containing no information that proves they have it. So you realise it must be a two-step process.

You should also realise that it is impossible to avoid asking at least one gazelle if they have the virus.

It therefore sounds impossible, since no-one can be surveyed anonymously. But there IS a loophole. While it's true you cannot keep the answer a secret...the real genius lies in the realisation that what needs to be kept secret is the QUESTION.

And the best way to that is to ask one of two questions, and leave it up to chance regarding which one gets asked, to create plausible deniability for the surveyed gazelles. So let's introduce a random element, such as tossing a coin.




Get your surveyed gazelle to toss a coin. If heads, ask if they have Geo-orgosis. If tails, get them to toss the coin again, and ask "Did you get heads on your second toss?"

Regardless of whatever was asked, divide all answers into yes's and no's (with names written alongside each answer of course). Since a binary yes or no is all that is being recorded, the government, if suspicious, can easily contact them and verify they answered truthfully, without them actually knowing what it was they were being asked.

Maths time! 



Let's say we surveyed 1000 gazelles and got 450 yes's and 550 no's. The odds of a coin flip is 50:50, so give or take a margin of chance, 50% of the gazelles will not have been asked if they have the virus, and so got asked if they got heads on the second toss. And the odds of getting heads again is also 50:50, so those who got asked the other question should, give or take, return with 250 yes's and 250 no's.

We then deduct that from the main pile to get 200 yes's and 300 no's, to represent those who got asked if they have Geo-orgosis. But that's only half the surveyed population, so we double this, to 400 yes's and 600 no's.

As always, like any good survey, the larger your sample size, the more accurate and reliable your end results will be.

So we have our accurate survey of how far the virus spread, a record of everyone's answer, and nothing to suggest to the government that they have the virus.