9,73,241,561,1081,1849,_?_ • Hacker News Board

Re: 9,73,241,561,1081,1849,_?_

#71

Post by viraptor » Thu, Nov 05, 2009, 11:32 PM UTC

edw519 wrote: post #32

amichail wrote: post #11

This question is not well-defined. Any number can be a solution.

This question is not well-defined. It's defined just well enough to identify you as someone who'd rather debate the problem than attack it. In other words, it has done its job.

Is it defined well enough to allow you to draw that kind of conclusions without any context?

What if that question was meant to find people who think about what is the real goal and asking "are we thinking about the same thing, or should we agree on more details" instead of attacking the problem at hand. Otherwise "0" is a perfectly good answer (for any reason).

This discussion has as much sense as a typical IQ test... (~nil)

Re: 9,73,241,561,1081,1849,_?_

#72

Post by jcl » Fri, Nov 06, 2009, 12:07 AM UTC

alain94040 wrote: post #50

bdr wrote: post #14

Earlier quoted context omitted.

Here's one interpretation: What will the simplest program that outputs these numbers output next?

print "9,73,241,561,1081,1849,0". So 0 is the answer. Actually, any digit, so I don't waste one extra character in my program. Did I win?

Sorry, the APL program is only 26 characters:

  +/1 ¯4 4 8×[2](⍳9)∘.*¯1+⍳4

And outputs:

  9 73 241 561 1081 1849 2913 4321 6121

Re: 9,73,241,561,1081,1849,_?_

#73

Post by jcl » Fri, Nov 06, 2009, 12:21 AM UTC

g__ wrote: post #63

bdr wrote: post #22

Earlier quoted context omitted.

Well, that could be done by brute force. Realistically, though, it's more about whether anyone can beat your answer.

You'd have to determine if a program halts. Unless you restrict to non-Turing-complete language, this is undecidable.

You can simply modify your definition of "simplest" to be "shortest that completes in a million steps" or some such. A program that takes so long to finish that you're not sure it will return your desired value is probably not the simplest.

Re: 9,73,241,561,1081,1849,_?_

#74

Post by jacobolus » Fri, Nov 06, 2009, 1:06 AM UTC

osteele wrote: post #60

The wonderful (satirical, but mathematically sophisticated) book Mathematics Made Difficult introduces difference tables, and uses them to demonstrate how to compute the next number in the sequence [1,2,4,8,16,…] – that number being, of course, 31. This answer is correct in that it is the next item in the lowest-order polynomial that generates the first five terms. This reveals both the strength and weakness of diffe…

How does that work? Like this? That's not really following the "pattern" though, which is to keep adding 1 down the left edge of the triangle. Choosing to put a 0 in because we ran out of terms in our series is pretty arbitrary.

    1  2  4  8 16 31
     1  2  4  8  15
       1  2  4  7
        1  2  3
          1  1
           0

Re: 9,73,241,561,1081,1849,_?_

#75

Post by Wilduck » Fri, Nov 06, 2009, 1:30 AM UTC

moron4hire wrote: post #24

Not to be too harsh here, but... I've been using "difference tables" (without calling it that) since I was 10 years old. I don't mean this to be bragging at all, because I didn't think (and still don't think) it was at all remarkable. It's just a basic method of analysis.

Learned them in 5th grade "wings" class in Minnesota.

Re: 9,73,241,561,1081,1849,_?_

#76

Post by rw » Fri, Nov 06, 2009, 1:31 AM UTC

megamark16 wrote: post #12

fsniper wrote: post #4

I hit my head to wall after reading this. Difference table is a really cool way to solve this kind of questions. I thought "how come I have never learned this difference table before". I could make better points with IQ tests with difference tables :)

I've never been particularly good (or confident?) at math, but this actually piqued my interest, it's a very cool trick/technique. Maybe I should enroll in a math class at the local community college just to try to improve myself a little bit. Besides, I have so many more ways to actually apply what I'd be learning now then I did when I took my last math class (which I think was back when I was 16 or 17).

You'll probably get farther with self-study. I suggest picking a field or two (discrete mathematics, number theory, graph theory, topology, and abstract algebra are probably the most useful and accessible ones to you right now) and then meeting with a professor a few times a month to go over homework problems.

Doing it that way will prepare you to teach yourself the material, giving you the confidence you claim you don't yet have.

Re: 9,73,241,561,1081,1849,_?_

#77

Post by albertsun » Fri, Nov 06, 2009, 2:50 AM UTC

http://www2.research.att.com/~njas/sequences/

This is a great resource for finding information on integer sequences significant in combinatorics and other formal math topics. It didn't have the solution to this particular sequence, because, afaik there is nothing particularly interesting about it.

Re: 9,73,241,561,1081,1849,_?_

#78

Post by psyklic » Fri, Nov 06, 2009, 3:04 AM UTC

albertsun wrote: post #77

http://www2.research.att.com/~njas/sequences/ This is a great resource for finding information on integer sequences significant in combinatorics and other formal math topics. It didn't have the solution to this particular sequence, because, afaik there is nothing particularly interesting about it.

Also of note is their Superseeker computer -- email it your sequence and it will perform a lot of additional analyses on the sequence beyond the normal web interface.

http://www2.research.att.com/~njas/sequences/ol.html

Re: 9,73,241,561,1081,1849,_?_

#79

Post by req2 » Fri, Nov 06, 2009, 4:51 AM UTC

jacobolus wrote: post #74

osteele wrote: post #60

The wonderful (satirical, but mathematically sophisticated) book Mathematics Made Difficult introduces difference tables, and uses them to demonstrate how to compute the next number in the sequence [1,2,4,8,16,…] – that number being, of course, 31. This answer is correct in that it is the next item in the lowest-order polynomial that generates the first five terms. This reveals both the strength and weakness of diffe…

How does that work? Like this? That's not really following the "pattern" though, which is to keep adding 1 down the left edge of the triangle. Choosing to put a 0 in because we ran out of terms in our series is pretty arbitrary. 1 2 4 8 16 31 1 2 4 8 15 1 2 4 7 1 2 3 1 1 0

Difference tables don't operate on a "pattern"- they simply take the difference of the two terms above.

Re: 9,73,241,561,1081,1849,_?_

#80

Post by roundsquare » Fri, Nov 06, 2009, 5:59 AM UTC

Is there interest in people posting neat math puzzles on HN more frequently? There's a few I really like and I would love to see what puzzles others have.