Proving you can't make 2011 out of 1,2,3,4 | Hacker News Reader

Proving you can't make 2011 out of 1,2,3,4

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

Make an answer.

switz if he was around 370 years ago:

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

And I'm reminded I suck at math.

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.

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?

I read it as, "an arbitrary number of factorials that can be different for each number."

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

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

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

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

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

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.

Oh, I totally misread that sentence.

2011 can be made from numbers 4 and 5:

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

They need to be in the correct order though.

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

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

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

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.

think are doing: reddit, hn, etc.

supposed to be doing: what the post indicates. Grading papers. (dis)proving p != np. (dis)proving one of the other millennium problems.

EDIT: formatting.

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