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You gave up trying to get the recipes, and go home. You get on Puzzling.SE to find your friend has been recording all your attempts (and his elephant failures).

You also find when you try to log into Puzzling.SE You get redirected to a question called "Security to your account!"

The body goes like this:

You try to get on Puzzling.SE so you can answer puzzles but find that a hacker has set up a password system. You wait to listen to traffic to see how he lets people in.

While analyzing traffic packets (You little hacker!) you get the following responses:

"5" -> "Impossible"
"6" -> "Impossible"

Then some bright guy who's also analyzing traffic thinks he's got it.

"0" -> "Impossible"

His computer then shuts down forever.
Nobody else comes for a while so it's your turn now!
Your question is "Infinity". What's your answer? Also, what was the correct answer to 0? Why?

To get it you know you have to answer the question. What is the answer?

Hints:

What is and what can't is elementary.

Let it be known there are inverse operations!

You are in the basic math division.

BonusResponses:

"7" -> "Impossible"

"8"-> "Impossible"

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  • $\begingroup$ Can you maybe give an example of a correct, different answer? $\endgroup$ – Ry- Nov 13 '14 at 18:43
  • $\begingroup$ @mini If no one gets it I will as a hint. $\endgroup$ – warspyking Nov 13 '14 at 18:46
  • $\begingroup$ In my opinion, this kind of puzzle is more fun if I have more data to think about. With only 3 or 4 data points there are bound to be simple answers that fit the data but that you won't accept. $\endgroup$ – Lopsy Nov 13 '14 at 21:13
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    $\begingroup$ Based off of the information, a correct answer is "Given a number n, the answer is n/(n-n)." I feel like this is incorrect (hopefully it is), yet it fits every single requirement. $\endgroup$ – mdc32 Nov 14 '14 at 1:21
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    $\begingroup$ could also be sqrt(-x), only allows negative numbers and 0 $\endgroup$ – Falco Nov 14 '14 at 12:55
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I think it is

0=0 Infinity=Impossible/Undefined

Thinking:

Arcsin 0=0 and arcsin infinity is undefined. Arcsin's inverse is sin.

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  • $\begingroup$ Sorry, if it's possible there IS a number response. $\endgroup$ – warspyking Nov 13 '14 at 20:53
  • $\begingroup$ Can you add a hint? $\endgroup$ – QuyNguyen2013 Nov 13 '14 at 20:59
  • $\begingroup$ For every wrong answer I will add a new hint. $\endgroup$ – warspyking Nov 13 '14 at 21:12
  • $\begingroup$ @warspyking I changed my answer $\endgroup$ – QuyNguyen2013 Nov 13 '14 at 22:40
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    $\begingroup$ could be the reverse of any function which doesn't result in 5-8 as outputs but includes 0 (for example all functions which output 0-1, sin, cos, or -x^2) $\endgroup$ – Falco Nov 14 '14 at 12:54
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I've solved it.

The correct response is always "impossible".

The computer shut down because of a coincidental hardware failure and the correct answer to 0 is thus "impossible".

I think my answer fits every case so far.

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The solution is:

0-0

Because:

Five and Six can have opposites, but 0 can't.

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  • $\begingroup$ This makes no sense. Your because does not even describe the solution. $\endgroup$ – QuyNguyen2013 Nov 13 '14 at 21:23
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The question is:

Can you determine the image of this number if we consider an arbitrary 1-1 function on the set of integer numbers?

And the answers are:

0 -> 0, infinity -> "impossible".

Of course, this won't be the right answer, but this one sounds good to me. :-)

Previous attempt

The question is:

What does the number divided 0 times equals to?

The answers are:

"0" -> 1, "infinity" -> "Impossible". I'm not that sure about the second answer; the first should work with every number, not only "1".

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  • $\begingroup$ Ex: 0 divided by 0 is an intermediate state. 1 divided by 0 is also an intermediate state, or infinity. Id this is true, the question makes no sense. $\endgroup$ – QuyNguyen2013 Nov 13 '14 at 21:29
  • $\begingroup$ Sorry, I can't understand what did you mean, can you explain me better? It'd be very appreciated. $\endgroup$ – user1962 Nov 13 '14 at 21:36
  • $\begingroup$ Zero divided does not equal 1. 0x9=0 so shouldn't, 0 divided by 0 return 9? Or 8? Etc. $\endgroup$ – QuyNguyen2013 Nov 13 '14 at 21:38
  • $\begingroup$ I specified it. However, now I'll try to think about a plausible answer. $\endgroup$ – user1962 Nov 13 '14 at 21:44

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