A Quick Puzzle to Test Your Problem Solving • Hacker News Board

Re: A Quick Puzzle to Test Your Problem Solving

#251

Post by GhotiFish » Fri, Jul 03, 2015, 1:32 AM UTC

monjaro wrote: post #190

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,…

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 to the principa mathematica that I'm actually referring to principa quus? If I then describe axiom 1 can you not know my words are referring to axiom quus?

It seems the only power of this assertion is that language provides no absolute common ground.

Am I understanding this correctly?

Re: A Quick Puzzle to Test Your Problem Solving

#252

Post by thaumasiotes » Fri, Jul 03, 2015, 1:40 AM UTC

ddlatham wrote: post #236

thaumasiotes wrote: post #185

Earlier quoted context omitted.

Not so. http://mathworld.wolfram.com/MonotoneIncreasing.html

So. http://mathworld.wolfram.com/MonotonicFunction.html https://en.wikipedia.org/wiki/Monotonic_function

You think the definition of "monotonic function" is more relevant to the meaning of "monotonically increasing sequence" than the definition of "monotone increasing" is?

[1,1,2], [1,1,1], and [1,2,2] are not monotone increasing. They're also not monotonic functions.

Re: A Quick Puzzle to Test Your Problem Solving

#253

Post by Myrmornis » Fri, Jul 03, 2015, 1:46 AM UTC

ddlatham wrote: post #3

I'm curious to see more about the distribution of questions and answers people had, and how the HN population may differ from the NYT's. There will certainly be self selection bias here, but if you're willing to share how you did with others, please enter it here: https://docs.google.com/forms/d/17e5BIL0lH8OHsGj89Zdtdl8GeCV... The result summary is visible here: https://docs.google.com/forms/d/17e5BIL0lH8OHsGj89Zdtdl…

It would be relevant to include a histogram of #yes_answers - #no_answers in the summary, to test whether people are biased towards positive rather than negative tests. I think the raw data suggests that it does although I totally failed to create a histogram in google spreadsheets within 5 minutes.

Re: A Quick Puzzle to Test Your Problem Solving

#254

Post by odonnellryan » Fri, Jul 03, 2015, 1:50 AM UTC

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,…

Tests like this are frustrating even if you don't recognize the logical fallacy! Just because it's always possible you're wrong. You're either right because you're lucky, or wrong because you messed up!

Re: A Quick Puzzle to Test Your Problem Solving

#255

Post by Sadgrinner » Fri, Jul 03, 2015, 2:00 AM UTC

thaumasiotes wrote: post #252

ddlatham wrote: post #236

Earlier quoted context omitted.

So. http://mathworld.wolfram.com/MonotonicFunction.html https://en.wikipedia.org/wiki/Monotonic_function

You think the definition of "monotonic function" is more relevant to the meaning of "monotonically increasing sequence" than the definition of "monotone increasing" is? [1,1,2], [1,1,1], and [1,2,2] are not monotone increasing. They're also not monotonic functions.

In all seriousness, the definition of monotonically increasing that I was taught is the same as exists in wikipedia:

"A function is called monotonically increasing (also increasing or non-decreasing), if for all x and y such that x https://en.wikipedia.org/wiki/Monotonic_function#/media/File...

This definition allows for 'flatness' in a graph, since the derivative does not change sign.

Or, from http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/... :

    A sequence f(n) is monotonic increasing if f(n+1) ≥ f(n) for all n ∈ N.
    The sequence is *strictly* monotonic increasing if we have > in the definition instead of ≥.

Re: A Quick Puzzle to Test Your Problem Solving

#256

Post by techonup » Fri, Jul 03, 2015, 2:21 AM UTC

tikhonj wrote: post #250

tjohns wrote: post #203

Earlier quoted context omitted.

1, 1, 1 was actually the test case that clued me in that n^1, n^2, n^3 couldn't be the right solution.

n=1? But I totally see why it would cause you to pause and rethink your original idea :).

The point is that it didn't work, so exponentiation was out the window.

Re: A Quick Puzzle to Test Your Problem Solving

#257

Post by arikrak » Fri, Jul 03, 2015, 2:26 AM UTC

the questions is somewhat ambiguous. it would be more interesting to see what happens of people really understood the question and if they had a real motivation to get it correct.

Re: A Quick Puzzle to Test Your Problem Solving

#258

Post by beatbrokedown » Fri, Jul 03, 2015, 3:01 AM UTC

ddlatham wrote: post #3

I'm curious to see more about the distribution of questions and answers people had, and how the HN population may differ from the NYT's. There will certainly be self selection bias here, but if you're willing to share how you did with others, please enter it here: https://docs.google.com/forms/d/17e5BIL0lH8OHsGj89Zdtdl8GeCV... The result summary is visible here: https://docs.google.com/forms/d/17e5BIL0lH8OHsGj89Zdtdl…

My fuzzing went:

8 4 2 (no) 1 2 3 (yes) 1 1 1 (no) 1 100 123 (yes) 1.0 1.1 1.2 (yes)

answer: incrementing numbers

Re: A Quick Puzzle to Test Your Problem Solving

#259

Post by thaumasiotes » Fri, Jul 03, 2015, 3:22 AM UTC

Sadgrinner wrote: post #255

thaumasiotes wrote: post #252

Earlier quoted context omitted.

You think the definition of "monotonic function" is more relevant to the meaning of "monotonically increasing sequence" than the definition of "monotone increasing" is? [1,1,2], [1,1,1], and [1,2,2] are not monotone increasing. They're also not monotonic functions.

In all seriousness, the definition of monotonically increasing that I was taught is the same as exists in wikipedia: "A function is called monotonically increasing (also increasing or non-decreasing), if for all x and y such that x https://en.wikipedia.org/wiki/Monotonic_function#/media/File... This definition allows for 'flatness' in a graph, since the derivative does not change sign. Or, from http://www-history.mcs…

You can draw that contrast (increasing vs strictly increasing), but what I was taught was to contrast increasing functions/sequences with nondecreasing functions/sequences.

A book or paper will make it clear what they mean by "increasing" by using the definition. There, it doesn't matter at all -- they could just as easily coin new words, since they immediately give the full definition. But the people hanging around this thread, telling people who are using a very common definition of "monotonically increasing" that (in paraphrase) "I hate to be pedantic, but you've made a mistake, in that I would have phrased that differently" have failed to contribute anything or to be pedantically correct. There's no case to be made that, if I say a "monotonically increasing sequence" must be increasing rather than nondecreasing, I've made a terminological mistake. This is a term with different definitions in different treatments.

Re: A Quick Puzzle to Test Your Problem Solving

#260

Post by nandemo » Fri, Jul 03, 2015, 3:29 AM UTC

yequalsx wrote: post #199

perlgeek wrote: post #165

Earlier quoted context omitted.

Yes and yes. It wouldn't activate the "check" button with complex numbers.

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.