

Proving you can't make 2011 out of 1,2,3,4 - SandB0x
http://math.stackexchange.com/questions/92230/proving-you-cant-make-2011-out-of-1-2-3-4-nice-twist-on-the-usual

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kokey
I have discovered a truly marvelous proof of this, which this comment box is
too small to contain.

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switz
Make an answer.

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kenjackson
switz if he was around 370 years ago:

"Fermat, I have a blank sheet of paper right here."

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PhrosTT
And I'm reminded I suck at math.

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Jun8
The math level of Ron Maimon's answer is a at college undergraduate level at
best, it's just a case of patiently enumerating a lot of different cases. In
fact I think this is more of a CS question than a math one. It would be
interesting to ask a similar question, limiting it to four operations, to a
good interview candidate to see how they handle expression parsing and case
analysis.

Tangentially, Ron's answers on Physics Exchange are consistently among the
best, I think he has the highest reputation there.

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pavel_lishin
What do the ellipses (...) signify in his answer? Does it just mean an
arbitrary number of factorials, so long as it's the same for each number?

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nialo
They just indicate some arbitrary number of factorials, with no particular
restrictions.

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hardik988
One of the problems in my AI class was to solve this was using genetic
algorithms - which seem a perfect way to solve such problems because the
intended goal is already known.

A similar problem (with lesser constraints), is :

Given the digits 0 through 9 and the operators +, -, * and /, find a sequence
that will represent a given target number. The operators will be applied
sequentially from left to right as you read.

which is explained at <http://www.ai-junkie.com/ga/intro/gat3.html>

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pavel_lishin
Perhaps we should update the title, since someone did solve it for n = 4.

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kijin
If you're referring to the second comment, it seems that he used operators not
permitted by OP.

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pavel_lishin
I was talking about "Ron Maimon's heroic attempt" - though I admit that I'm
not sure what the ... represents.

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sp332
The heroic attempt has not been finished (since you can include any arbitrary
number of factorials). It will only be finished when an example is found, or
when someone proves that (as stated in the question): _2011 cannot be written
as 3!!!...!!! ∗ 4!!!!...!!! / 3!!!!...!!! for any choices of numbers of
factorials._

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pavel_lishin
Oh, I totally misread that sentence.

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merraksh
2011 can be made from numbers 4 and 5:

    
    
      5*5*4*5*4 + 5*4 - 5 - 4

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MetallicCloud
They need to be in the correct order though.

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spelunker
Is this what math-inclined people spend their free time doing? Goodness...

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xyzzyz
May I ask what did you think mathematicians are doing, and what do you think
they are supposed to be doing?

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sukuriant
You're right. It's terrible for mathematicians to be spending time solving
silly things that interest them.

Pardon me while I return to writing a Game of Life simulator

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xyzzyz
What I actually meant is that almost all mathematical problems are on some
level silly, and most of mathematicians solve them precisely because they find
them interesting. In this case the silliness is clearly visible to a layman,
but in more abstract parts of math one needs to spend quite a lot of time to
understands the underlying concepts.

