5 ms·
Proving you can't make 2011 out of 1,2,3,4
- pavel_lishin 15y agoPerhaps we should update the title, since someone did solve it for n = 4.
- kijin 15y agoIf you're referring to the second comment, it seems that he used operators not permitted by OP.
- pavel_lishin 15y agoI was talking about "Ron Maimon's heroic attempt" - though I admit that I'm not sure what the ... represents.
- sp332 15y agoThe 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.
- pavel_lishin 15y agoOh, I totally misread that sentence.
- PhrosTT 15y agoAnd I'm reminded I suck at math.
- Jun8 15y agoThe 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.
- pavel_lishin 15y agoWhat 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?
- redthrowaway 15y agoI read it as, "an arbitrary number of factorials that can be different for each number."
- nialo 15y agoThey just indicate some arbitrary number of factorials, with no particular restrictions.
- spelunker 15y agoIs this what math-inclined people spend their free time doing? Goodness...
- xyzzyz 15y agoMay I ask what did you think mathematicians are doing, and what do you think they are supposed to be doing?
- sukuriant 15y agoYou'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
- xyzzyz 15y agoWhat 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.
- younata 15y agothink 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.
- kokey 15y agoI have discovered a truly marvelous proof of this, which this comment box is too small to contain.
- switz 15y agoMake an answer.
- kenjackson 15y agoswitz if he was around 370 years ago: "Fermat, I have a blank sheet of paper right here."
- switz 15y agoMake an answer.
- hardik988 15y agoOne 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 http://www.ai-junkie.com/ga/intro/gat3.html
- merraksh 15y ago2011 can be made from numbers 4 and 5: 5*5*4*5*4 + 5*4 - 5 - 4
- MetallicCloud 15y agoThey need to be in the correct order though.