

The world simplest impossible problem (pdf) - helwr
http://www.mathworks.com/clevescorner/dec1990

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Joakal
[http://www.wolframalpha.com/input/?i=+%28+x+%2B+y%29+%2F+2+%...](http://www.wolframalpha.com/input/?i=+%28+x+%2B+y%29+%2F+2+%3D+z)

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robertk
Right. The best thing you can do is say the numbers are an element of the set
of tuples {(x, 6-x) : x \in R}. And that's only if you restrict to reals.
Consider the fact that the "average" of i and 6-i is also 3. In general, you
replace R by k, where k is your field (or even any unital ring where 2 = 1+1
is invertible). Thus, in the finite field F_5, the possible numbers are (0,1),
(1,0), (2,4), (4,2), (3,3). More cleanly, you can take the k-points on the
variety x + y - 6 = 0.

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noobiscus
Certain I'm not the only one who raised an eyebrow at "it's a matrix problem"
and the cranking out of Matlab to find solutions to x+y = 6

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JonnieCache
To be fair it was written by the co-founder of the company that does MATLAB.
That's kinda the point of the article.

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atakan_gurkan
My answer to his question at the end of the essay would be "0, π and 2π".
Strangely, this triple is the only one that looks nice to me, even though all
of "3 and 3", "0 and 6" and "2 and 4" as well as coming up with a pair with
long decimals looks OK to me for the original question.

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Vivtek
I used his cheat solution and went with π, π, and π.

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imurray
[1990]

The 2010 followup on _compressed sensing_ :
[http://www.mathworks.com/company/newsletters/articles/cleves...](http://www.mathworks.com/company/newsletters/articles/clevescorner-
compressed-sensing.html)

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ZackOfAllTrades
This has the feeling of a pun where the person says something garbled and then
starts laughing and pointing when you don't understand what he said.

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brakon
why all the fuss, a solution would be just 2,4 , they didnt even get to that

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nicolasp
Actually they did: "But three other people all said "2 and 4". That is
certainly another "nice" answer, but the constraints it satisfies are more
subtle. They have something to do with requiring the solution to have integer
components that are distinct, but near the specified average. It's harder to
state and compute the solution in MATLAB without just giving the answer."

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Vivtek
In English, when you say you have two "somethings", they're generally
considered distinct. This is one of the gotchas when translating between
English and math.

