The world simplest impossible problem (pdf)

http://www.mathworks.com/clevescorner/dec1990

by helwr • 15 years ago

44 11 15 years ago

Joakal• 15 years ago

http://www.wolframalpha.com/input/?i=+%28+x+%2B+y%29+%2F+2+%...

robertk• 15 years ago

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.

noobiscus• 15 years ago

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

JonnieCache• 15 years ago

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

atakan_gurkan• 15 years ago

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.

Vivtek2• 15 years ago

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

brakon• 15 years ago

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

nicolasp• 15 years ago

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."

Vivtek2• 15 years ago

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.

imurray• 15 years ago

[1990]

The 2010 followup on compressed sensing: http://www.mathworks.com/company/newsletters/articles/cleves...

ZackOfAllTrades• 15 years ago

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.

The world simplest impossible problem (pdf)

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