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

Re: A Quick Puzzle to Test Your Problem Solving

#271

Post by eru » Fri, Jul 03, 2015, 4:46 AM UTC

nandemo wrote: post #265

scarmig wrote: post #192

Earlier quoted context omitted.

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…

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.

Re: A Quick Puzzle to Test Your Problem Solving

#272

Post by eru » Fri, Jul 03, 2015, 4:50 AM UTC

yvsong wrote: post #239

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,…

With an equal protection clause, i.e., no particular number or a group of numbers can appear in the rule, is the problem solvable?

Depends on what rules you allow.

What you want to forbid is not so much mentioning specific numbers, but you want to only allow rules that have certain symmetries. Eg you can require tranlation invariance

    rule(x, y, z) = rule(x+offset, y+offset, z+offset)

to restrict the set of rules.

Re: A Quick Puzzle to Test Your Problem Solving

#273

Post by ddlatham » Fri, Jul 03, 2015, 4:50 AM UTC

eru wrote: post #268

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…

Thanks for setting up the survey! Could you perhaps move to a bar chart instead of pie charts?

Don't think that's an option for Google docs - but feel free to take the data and share one.

Re: A Quick Puzzle to Test Your Problem Solving

#274

Post by eru » Fri, Jul 03, 2015, 4:50 AM UTC

smilefreak wrote: post #261

Does laziness have anything to do with the responses? You get a rule that seems to work and so you seek the reward early. It takes effort to prove yourself wrong. I was trapped by this and guessed it was exponential series n^1,n^2 etc for n starting at greater than 2. While technically true this was not the rule they had in mind.

Why is it technically true?

Re: A Quick Puzzle to Test Your Problem Solving

#275

Post by eru » Fri, Jul 03, 2015, 4:54 AM UTC

pizza wrote: post #158

phantarch wrote: post #81

Funnily enough, I notice confirmation bias quite a bit in a D&D game I am currently DM of. I'm playing with a group of friends who are big into video games, and as a result they consistently seek resolutions to conflicts in D&D by way of what they know from shooters: kill everything in sight. Yes, it's at times a valid answer, but it's not the only one and it's certainly not the most interesting one. The best way tha…

Maybe some positive/negative feedback built into the campaign could help; e.g. for each act of benevolence/violence, add/subtract a 'karma' point from some running total, and alter the gameplay as needed.

Just don't tell them explicitly about it. (That'd be taking away all the fun.)

Re: A Quick Puzzle to Test Your Problem Solving

#276

Post by eru » Fri, Jul 03, 2015, 4:55 AM UTC

FilterJoe wrote: post #140

While the HN crowd mostly gets this right when framed as a math puzzle, my guess is that confirmation bias is alive and well in high tech just like in any other field. One example: Young 20s entrepreneur vs. early 50s entrepreneur. Without knowing anything about either person, which startup is more likely to succeed? Even if you have the business plans for both, and you meet both - which one are you going to be more…

I'd trust the older guy.

Re: A Quick Puzzle to Test Your Problem Solving

#277

Post by eru » Fri, Jul 03, 2015, 4:56 AM UTC

Tloewald wrote: post #238

brianwillis wrote: post #235

This doesn't seem to work right for negative numbers. The article says the rule is "each number must be larger than the one before it", but if you try -2 -4 -6 it says that pattern doesn't match the rule. Maybe I'm just being pedantic here, but last I checked -6 was larger than -4.

It works for floating point numbers -- 0.01 0.02 0.04 for example. So it's a geometric series that has to start with a positive number and doubles. (The submit button and the show the answer button were broken for me.)

That's unintentionally hilarious.

Re: A Quick Puzzle to Test Your Problem Solving

#278

Post by ddlatham » Fri, Jul 03, 2015, 5:00 AM UTC

thaumasiotes wrote: post #259

Sadgrinner wrote: post #255

Earlier quoted context omitted.

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…

Thanks for your perspective. It's interesting that there appears to be ambiguity in the terms and a diversity in what is being taught.

Re: A Quick Puzzle to Test Your Problem Solving

#279

Post by smilefreak » Fri, Jul 03, 2015, 5:07 AM UTC

eru wrote: post #274

smilefreak wrote: post #261

Does laziness have anything to do with the responses? You get a rule that seems to work and so you seek the reward early. It takes effort to prove yourself wrong. I was trapped by this and guessed it was exponential series n^1,n^2 etc for n starting at greater than 2. While technically true this was not the rule they had in mind.

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?

Re: A Quick Puzzle to Test Your Problem Solving

#280

Post by tikhonj » Fri, Jul 03, 2015, 5:08 AM UTC

techonup wrote: post #256

tikhonj wrote: post #250

Earlier quoted context omitted.

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.

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