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A Quick Puzzle to Test Your Problem Solving

nytimes.com

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Re: A Quick Puzzle to Test Your Problem Solving

#291

Post by IshKebab »

Kenji wrote: post #26

"We’ve chosen a rule that some sequences of three numbers obey — and some do not. Your job is to guess what the rule is." My mistake was to assume that choosing the first number uniquely defines the next ones in the sequence. Since, you know, like all the sequence puzzles I've seen before worked like that, and I didn't read it rigorously enough. Oh, by the way, the doubling thing is wrong if you use negative numbers…

Yeah I thought it would be something like "Numbers must strictly increase unless the first number is 15326". Then the point of the article would be that some government rules are not well defined.

Re: A Quick Puzzle to Test Your Problem Solving

#292

Post by Matumio »

GhotiFish wrote: post #251
monjaro wrote: post #190

Earlier quoted context omitted.

This has nothing to do with Gödel's incompleteness theorem. It's much simpler than that: https://en.wikipedia.org/wiki/Wittgenstein_on_Rules_and_Priv...

Thanks for the link! That was an interesting read, but I don't think I understand the premise of the argument. From the article ... It is perfectly consistent with your previous use of 'plus' that you actually meant it to mean the 'quus' function, ... That may be true, but only if you assume I'm not referring to the plus derived from the axioms of principa mathematica. I am. Is it then the question that when I refer…

This makes my head hurt. Surely Wittgenstein had permission to use Occam's razor? I mean, if it's possible that you actually meant quus_5 then it's equally possible that you meant quus_3 or quus_114, but since you didn't mention that, I will just assume you meant whichever requires the least amount of parameter-guessing from my side. After all, you have written it down for a human receiver, not for an alien from the Quus_8th dimension.

Re: A Quick Puzzle to Test Your Problem Solving

#294

Post by tripzilch »

TeMPOraL wrote: post #40
cabirum wrote: post #23

function judgeSentence(sentence, numNo) var probablyWrong = ["doubl", "expon", "multipl", "^", " ", "power", "two", "2", "twice", "as big", "nth", "rais"]; var seemsRight = ["larger", "increas", "greater", "small", "less", "big", ">", " Been expecting something more interesting than that

It's surprising how far you can go by such heuristics. I run an IRC bot that uses matches like this (I'm working on a proper solution right now though) to parse natural language queries and I managed to trick few people into thinking they're talking with human. As long as it's ok for 90% of most common cases, people often won't notice.

I've made a robot that screams[0]. That is, just outputs a random string of "AAAAaaa" when its name is mentioned or when somebody else screams (four or more A's).

What is surprising is how basically 15 lines of python implementing these rules, invokes a very real emotional response in a lot of people :-)

I named it "Wilhelm".

[0] inspired by this comic http://gunshowcomic.com/513

Re: A Quick Puzzle to Test Your Problem Solving

#296

Post by nandemo »

eru wrote: post #271
nandemo wrote: post #265

Earlier quoted context omitted.

How about this? Choose a programming language. Choose a sequence prefix (in your example: 2, 3). Then consider all the programs that accept n as input and output a sequence of n numbers, such that the first numbers are always 2, 3. Now take the shortest of those programs. The sequence it produces is the "simplest". If this sounds tedious to code, you could easily outsource via Odesk or something.

You are asking for https://en.wikipedia.org/wiki/Kolmogorov_complexity It's uncomputable in general.

I know. :-)

Re: A Quick Puzzle to Test Your Problem Solving

#297

Post by yequalsx »

nandemo wrote: post #260
yequalsx wrote: post #199

Earlier quoted context omitted.

There isn't a way to check order for complex numbers in any reasonable way.

But the problem statement doesn't imply the rule involves ordering. Likely, it doesn't accept complex numbers (or vectors or matrices) as input as part of the (implicit) spec: in common parlance, "number" tends to mean real number.

The tests with real numbers indicate that the rule is one based on order. So the problem doesn't state this but it is easily deducible when working with real numbers. Hence no need to check complex numbers. In common parlance in mathematical circles "number" tends not to mean real number unless context makes this obvious.

Re: A Quick Puzzle to Test Your Problem Solving

#298

Post by nerdo »

Reminiscent of the folding table libertarians with their questionnaire and that political cartesian coordinate chart. "You answered that 'it's wrong to steal', [...psychobabble...], on this science graph it appears you've always secretly been a libertarian, we meet at the cinnabon on sundays".

Re: A Quick Puzzle to Test Your Problem Solving

#299

Post by elnion »

eru wrote: post #269
WildUtah wrote: post #223

Earlier quoted context omitted.

It accepts floating point numbers. To approximately double precision. But it accepts zero percent of real numbers.

I can nitpick better than that! To talk about a certain fraction of real numbers you have to have a distribution over them. In general we take the uniform distribution if no distribution is explicitly given. That doesn't work for real numbers (it doesn't even work for natural numbers). (See https://math.stackexchange.com/questions/14777/why-isnt-ther... ) If there's no implicit default distribution, we have to pick o…

Down the rabbit hole of pedantry: we don't need a distribution, just a measure, if we want to talk about how many reals it accepts. The Lebesgue measure is implied on the Reals if none is given, and the computable reals have measure zero.

We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.

Re: A Quick Puzzle to Test Your Problem Solving

#300

Post by elnion »

scarmig wrote: post #192
nothrabannosir wrote: post #173

My mathematical logic is rusty, but if I recall correctly, Gödel's incompleteness theorem basically states that it is impossible to solve this kind of question. No matter how many tests you run, there will always be an uncertainty. An incredibly stupid example is that the rule could be "yes for strictly increasing, OR if one of the numbers is -18273192783127897981." You'll never know. I understand this is contrived,…

Remotely related: I've been interested for awhile in how the same initial terms of a sequence could possibly be generated by multiple rules. For example, you might have 2,3... And the rest of the sequence might look like either 2,3,4,5,6... or 2,3,5,8,13... or 2,3,5,7,11... or even 2,3,5,10,20... Clearly, on some level those sequences are all much less complicated than one defined as "The first term is 2, the second…

This might be helpful: https://en.wikipedia.org/wiki/Generating_function

Generating functions provide a general framework for describing sequences, solving recurrence relations, etc.

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