The World's Simplest Impossible Problem. Moler, C. 1:92036v00+.
The World's Simplest Impossible Problem [link]Paper  abstract   bibtex   
If the average of two numbers is three, what are the numbers? The solution to this problem is not unique, and the problem is ill-defined, but that does not mean that MATLAB® cannot solve it. [] In this article from 1990, Cleve Moler explores this simple yet impossible problem and others like it using MATLAB to find answers with the fewest nonzero components and other ” nice” solutions.
@article{molerWorldSimplestImpossible1990,
  title = {The World's Simplest Impossible Problem},
  author = {Moler, Cleve},
  date = {1990},
  journaltitle = {MathWorks Technical Articles and Newsletters},
  volume = {1},
  pages = {92036v00+},
  url = {http://mfkp.org/INRMM/article/14226329},
  abstract = {If the average of two numbers is three, what are the numbers? The solution to this problem is not unique, and the problem is ill-defined, but that does not mean that MATLAB® cannot solve it.

[] In this article from 1990, Cleve Moler explores this simple yet impossible problem and others like it using MATLAB to find answers with the fewest nonzero components and other ” nice” solutions.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-14226329,aesthetic-value,ambiguity,computational-science,mathematical-reasoning,multiplicity,semantic-constraints}
}

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