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

Re: A Quick Puzzle to Test Your Problem Solving

#281

Post by MarkMc » Fri, Jul 03, 2015, 5:16 AM UTC

The comments here suggest people are missing the full significance of this problem. It's not just a cute number puzzle - it demonstrates a profound human weakness that has a deep impact in everything we do.

1. People that think having a gun in the house makes it safer will not try to design an experiment designed to demonstrate the opposite.

2. People who think organic food is better for you than regular food will not try to look for evidence that the two types of foods are equally healthy.

3. An Israeli who believes the area where he lives was uninhabited before 1948 is not going to think about what kind of evidence would contradict that belief.

I'm not saying the views above are incorrect. It's just that we are all guilty of falling in love with our beliefs when they should be mere acquaintances. Hence the quote, "People don't change their minds. They die, and are replaced by people with different opinions." [1]

[1] http://www.paulgraham.com/quo.html

Re: A Quick Puzzle to Test Your Problem Solving

#282

Post by [deleted] » Fri, Jul 03, 2015, 5:35 AM UTC

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…

[deleted]

Re: A Quick Puzzle to Test Your Problem Solving

#283

Post by firethief » Fri, Jul 03, 2015, 5:57 AM UTC

tikhonj wrote: post #280

techonup wrote: post #256

Earlier quoted context omitted.

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

My point was that 1,1,1 is 1^1,1^2,1^3 and actually fits the pattern :).

Right - by fitting the pattern but failing the actual criterion, it disproves the consecutive exponents hypothesis.

Re: A Quick Puzzle to Test Your Problem Solving

#284

Post by eru » Fri, Jul 03, 2015, 6:59 AM UTC

smilefreak wrote: post #279

eru wrote: post #274

Earlier quoted context omitted.

Why is it technically true?

As in every number in that set is a subset of the larger set of x < y < z. Poor language choice it's not true, yes I was wrong. I am just curious as to how much laziness and not necessarily confirmation bias has to do with the result. If getting it wrong had some kind of penalty or getting it right had some kind of reward ( money etc. ..), how much better would people do then?

Yes, it seems most people's rules actually were subsets of the true rule.

Laziness is involved to a certain degree. Though I don't know how much---no one is forcing anyone to do the puzzle, so the truly lazy filter out, too.

Re: A Quick Puzzle to Test Your Problem Solving

#285

Post by Ntrails » Fri, Jul 03, 2015, 8:51 AM UTC

eli wrote: post #213

perlgeek wrote: post #161

Earlier quoted context omitted.

So you limited yourself to non-negative integers, and had no idea what negative numbers or fractions would do.

Based on the context of the question and the UI of the testing interface, fractions seem unlikely to be an intended part of the question. I likewise wouldn't bother testing unicode U+216x roman numerals.

It refused to accept both fractions and imaginary numbers. I did test negatives and zeros since that was really the only remaining set I could think of.

Most importantly I used about 6 tests (3 right 3 wrong) to come up with the answer and then did another 17 looking for the trick. After all, it couldn't just be that simple right?

Re: A Quick Puzzle to Test Your Problem Solving

#286

Post by mordrax » Fri, Jul 03, 2015, 10:27 AM UTC

kittenfluff wrote: post #54

tmd wrote: post #7

It responds "No" to (10000000000000000, 10000000000000001, 10000000000000002) so the rule is not so simple after all :)

Responds "Yes" to 9007199254740990, 9007199254740991, 9007199254740992 but "No" to 9007199254740991, 9007199254740992, 9007199254740993 Presumably this is due to how Javascript handles integers, i.e. it uses the integer part of a float64, to wit > parseInt('9007199254740992') 9007199254740992 > parseInt('9007199254740993') 9007199254740992 Edit: I think this is the code that actually reads the numbers the user enters…

yeah alright.. i think someone didn't actually get the point of the article hehe

Re: A Quick Puzzle to Test Your Problem Solving

#287

Post by mordrax » Fri, Jul 03, 2015, 10:30 AM UTC

They don’t want to hear the answer “no.” In fact, it may not occur to them to ask a question that may yield a no.

So the author's obviously never heard of sanity checking, in fact that's the second thing that I always do once I confirm a solution is to confirm it's not a fallacy.

Having said that, my solutions were -10 -20 -40 -10 -8 -4 1024 1026 1030

and I said it was +2, +4 and got it wrong!

Re: A Quick Puzzle to Test Your Problem Solving

#288

Post by cristianpascu » Fri, Jul 03, 2015, 11:09 AM UTC

I understand the power of confirmation bias. I believe it to be natural for anyone. It's perfectly normal to seek an explanation that fits the already built cognitive structures, developed through experience. It's unreasonable to simply jump into new paradigms everytime we encounter a new fact. It takes time to prove that it doesn't fit, and then we start looking for new explanations.

However, the test simply required a possible solution. There are plenty solutions and it's absurd to think they have the simplest one. The simplicity of the rule is subjective, in that is evaluated differently by different people. The famous 'simple but no simpler' is relevant here. As long as we were not told to look for the simplest solution, ALL solutions are equally probable. That being the case, I started to with the first solution that popped into my mind. I sticked with that because of my psychological state. Some searched for other solutions.

I don't think that getting an YES was the main driving force. Of course it feels good to get an yes. This is fundamental in human relations. But it's not the whole story. People do not disbelief globar warming because they want to get an YES. The reason is much deeper. Just as many, so many people go to the wave of climate change because it's fashionable, it makes them feel good, accepted , part of the mainstream. Being a climate change denier is being a disident this day (not my flavor of disidentism), and being a disident is not for everyone. And perhaps disidents picking their fight have complicated reasons for doing so.

I went with the doubles.

Re: A Quick Puzzle to Test Your Problem Solving

#289

Post by nightcracker » Fri, Jul 03, 2015, 11:44 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,…

This does not hold - the test uses Javascript's numbers, which are finite. So it's theoretically possible to test every combination of inputs and convincingly answer what a possible rule is.

Re: A Quick Puzzle to Test Your Problem Solving

#290

Post by Yizahi » Fri, Jul 03, 2015, 11:53 AM UTC

pitchups wrote: post #76

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…

Intersting that the split of correct/wrong answers from the HN crowd is 78%/22% - the exact opposite of the general population : 22% / 78%! The HN community does think different :)

It just means that this test was described at least several times in different "computer" media over last few years and almost everyone has read about it. Same thing with all "logic" puzzles.