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Dr. Smith, having recently finished his PhD, called some of his friends that had just finished their doctorates and masters to comemorate in a trip to his uncle's country house.

During the party, the lights went out for roughly 10 minutes, and a loud noise could be heard. When the lights returned, Dr. Smith was the only one unaccounted for.

They found him dead in his room, with a gun on the floor and a bloodstained note stating, in his own handwriting, Smith's final problem:

There is a number that's 2 and 1, and neither
This number is 0 and 1, and both
This number is not easy to find, but do keep in mind that
To determine this number is to find the identity
This number should tell you who killed me.

The five friends that Smith called were named Ana, Eric, David, Gideon and Tatiana; among the staff only the butler, Mortimer, was present that day.

To give the friends peace of mind until the police solve this case, tell me: "Who killed Dr. Smith?"

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My guess is that

Dr. Smith committed suicide.

Argument:

* The bloodstained note hints at the imaginary unit $i$.
* It essentially states "The murderer is i", that is, "I am the murderer".
* The imaginary unit satisfies $i^2+1=0$ (with $2$ and $1$ and $0$).
* 0 and 1 are the coordinates of $i$ in the complex plane.
* In mathematics, the letters $i$ and $I$ are often used to denote the identity (for instance, in linear algebra $I$ is the identity matrix).

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  • $\begingroup$ That's not exactly the reasoning I had in mind but it works, and the answer is indeed correct! I hope this wasn't too easy (or too bad or something like that, for my first riddle here) :) $\endgroup$ – Chill Fruit Mar 20 '16 at 15:49
  • $\begingroup$ The puzzle is fine, in particular the red herrings Ana, Eric, David, Gideon and Tatiana and Mortimer. Perhaps you can also post the resoning you had in mind (as a separate answer)? $\endgroup$ – Gamow Mar 21 '16 at 11:41
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The answer was

that Dr. Smith killed himself, the number was i

Because

There is a number that's 2 and 1, and neither (It's 2-dimensional (complex), 1-dimensional (imaginary), and not actually 2 or 1.)
This number is 0 and 1, and both (It can be represented as $(0;1)$)
This number is not easy to find, but do keep in mind that (Complex)
To determine this number is to find the identity (If you represent a complex number as a matrix, its determinant will be $1$ )

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