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This question was asked in CSIR June 16.

Out of the following which one is the odd one out?

  • Cone
  • Torus
  • Sphere
  • Ellipsoid

Well in my point of view, cone, sphere and ellipsoid are topologically equivalent. So, answer should be torus. Am I right?

But some where I found answer cone since all other are 3-D representation of a circle.

Which one is correct?

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    $\begingroup$ There can be many different explanations, for example: cone is the only one that has corners $\endgroup$
    – Gintas K
    Jun 30, 2016 at 9:22
  • $\begingroup$ Yeah! that is why i am confused! is my explanation right ? $\endgroup$
    – Learner
    Jun 30, 2016 at 9:25
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    $\begingroup$ Torus can also be odd, because it's the only one without letter 'e' in it. As I told, many solutions, depending on your perspective :) $\endgroup$
    – Gintas K
    Jun 30, 2016 at 9:33
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    $\begingroup$ This is question is too broad and can be primarily opinion based. $\endgroup$
    – Adit Kirtani
    Jun 30, 2016 at 10:32
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    $\begingroup$ At first, this question seems too broad. However, it is presented as I got a different answer. Why? and that can be answered - as it already has been below - with You didn't. There are many good answers. This is a question about puzzles and not a puzzle in-and-of-itself, which fits well with Puzzling's original intent. $\endgroup$
    – Engineer Toast
    Jun 30, 2016 at 12:25

5 Answers 5

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The topologically equivalent explanation makes sense to me, since all the objects except the torus can be transformed into eachother.

On the other hand, as mentioned, there can be many different explanations.

The cone is the only one with a flat surface. The ellipsoid is the only one that can't be described using only circles.

But if you're a topologist, you can't distinguish between a teacup and a donut, and in this case the torus would seem like the odd one out.

(See here: https://books.google.dk/books?id=Kgnzwq62xv8C&pg=PT188&lpg=PT188&dq=donut+teacup&source=bl&ots=43lGVSh0zS&sig=27Nl0AaIFEabtiknBbKkWuGgkdg&hl=da&sa=X&ved=0ahUKEwiRoojwuM_NAhUG_ywKHeGFDFQQ6AEIITAB#v=onepage&q=donut%20teacup&f=false)

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The cone is the odd one out because it is the only one that isn't smooth and the only one that's of infinite extent (at least if you're a mathematician).

The torus is the odd one out because it's the only one that isn't simply connected.

The sphere is the odd one out because it's the only one on which euclidean symmetries act transitively (i.e., all its points are the same).

The ellipsoid is the odd one out because it's the only one on which some but not all points are umbilical points (i.e., points near to which the surface "looks like a sphere" in a certain sense).

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  • $\begingroup$ Technically an open cone is a smooth submanifold of $\mathbb{R}^3$, since it is an open subset. What is not a smooth submanifold, however, is the surface of that cone, in particular it is non-smooth exactly at the tip. $\endgroup$
    – Anon
    Jun 30, 2016 at 22:19
  • $\begingroup$ I was taking them all to be the surfaces. $\endgroup$
    – Gareth McCaughan ♦
    Jun 30, 2016 at 22:41
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Here is an alternative "All of the above" answer.

Since:

     Cone  cone
    Torus  torus
   Sphere  sphere / sphere   
Ellipsoid  ellipsoid / ellipsoid

We can say:

     this | is the only one containing...
----------+------------------------------
     Cone |         the pronoun one
    Torus |     1 other pronoun
   Sphere |    2 unique pronouns
Ellipsoid |  1 repeated pronoun
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    $\begingroup$ "I" is a pronoun that occurs twice in "Ellipsoid". $\endgroup$
    – Brian
    Jun 30, 2016 at 21:11
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    $\begingroup$ D'oh, how did I miss it, it's there twice! $\endgroup$
    – Jonathan Allan
    Jun 30, 2016 at 23:21
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Maybe

the torus,

because the other three are

quadric surfaces.

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Sphere is the odd one out because it is the only one that does not contain the letter 'o'.

As you can see, the question is completely ambiguous.

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