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

Re: A Quick Puzzle to Test Your Problem Solving

#201

Post by xenophon » Thu, Jul 02, 2015, 8:58 PM 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,…

I think the core idea is much simpler than that. It's the notion that falsifiability is the most powerful tool in our arsenal when we try to conceive of theories that explain a certain state of affairs.

The idea you're getting at is that no number of confirming observations can verify a universal generalization -- the reason why we continue to call generally accepted "truths" theories. But we can increase our certainty to the greatest degree possible by trying to test our hypothesis to the greatest degree we can.

Re: A Quick Puzzle to Test Your Problem Solving

#202

Post by the_af » Thu, Jul 02, 2015, 9:00 PM UTC

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…

It is true that, in general, this quiz is impossible to guess, for the reasons you explain.

But in this case -- which is the main point of the article -- it was actually a trivial rule. No tricks, no special cases. The real purpose wasn't for you to find the actual rule, but to learn about your biases. The only trick here lies in the human mind, and its tendency to validate patterns (and claim an early victory) instead of trying to refute them.

Re: A Quick Puzzle to Test Your Problem Solving

#203

Post by tjohns » Thu, Jul 02, 2015, 9:13 PM UTC

LoSboccacc wrote: post #132

benihana wrote: post #106

Earlier quoted context omitted.

I was just writing this out! I believe practice in unit testing is what let me get this question right. I almost submitted n^1, n^2, n^3 before I realized I didn't get any wrong answers and something didn't feel right. I credit this 'instinct' to having written thousands of tests, and trying to make them fail to make sure my tests weren't lying to me.

got tricked even if I tested 1, 1, 1

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.

Re: A Quick Puzzle to Test Your Problem Solving

#204

Post by mpu » Thu, Jul 02, 2015, 9:15 PM UTC

dhruvbird wrote: post #86

People try to make the fit be as tight as possible to the sample data -- the explanation is that simple. I don't buy the explanation provided in the article.

Pretty good point. That's how I felt.

Additionally, this setting is probably too close to usual situations you get in school where there is little to no interaction and negative answers from the teacher are seen as failures by students. (Speaking about education in my country only.)

Re: A Quick Puzzle to Test Your Problem Solving

#205

Post by tjohns » Thu, Jul 02, 2015, 9:17 PM UTC

yequalsx wrote: post #136

Math person here. I'm curious to know if anyone used decimal numbers in their tests and if negative numbers were used. The rule is increasing real numbers and one can guess that the rule is increasing numbers without realizing this includes all real numbers and not just integers. In addition to getting it right did you use an exhaustive set of tests?

I tested with negative integers, but didn't think to test with real numbers unfortunately. (Still got it right, but I should've tested that.)

That said, I did make sure to test all the edge cases I could think of. I was actually going to guess (n^1, n^2, n^3) at first, until it failed for (1, 1, 1).

10 "yes" tests, 6 "no" tests.

Re: A Quick Puzzle to Test Your Problem Solving

#206

Post by [deleted] » Thu, Jul 02, 2015, 9:21 PM 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,…

[deleted]

Re: A Quick Puzzle to Test Your Problem Solving

#207

Post by theVirginian » Thu, Jul 02, 2015, 9:24 PM UTC

I don't seem to be able to submit my answer or follow the link to see the answer for "just tell me the answer" is this supposed to be a trick or is my browser just not capable of properly following those links? Using Chromebook.

Re: A Quick Puzzle to Test Your Problem Solving

#208

Post by joezydeco » Thu, Jul 02, 2015, 9:26 PM UTC

tptacek wrote: post #168

joezydeco wrote: post #120

Earlier quoted context omitted.

Did you try floating point numbers? I didn't see anything in the text that said integers only.

I tried floating point numbers. Also, at 28 decimal places, the test breaks; it's not arbitrary precision. So, technically, the answer isn't simply "any ascending sequence of numbers".

Hah! Nice catch.

Re: A Quick Puzzle to Test Your Problem Solving

#209

Post by Nimitz14 » Thu, Jul 02, 2015, 9:27 PM UTC

damoncali wrote: post #143

Cool. The funny thing is I inserted a constraint of my own invention without even realizing it: "Use the fewest number of examples possible." Of course, this meant failing miserably, and was nowhere in the problem statement. Perhaps that's an additional factor - not exactly confirmation bias, but not unrelated.

Eliminating assumptions baby.

https://www.youtube.com/watch?v=9-9VLVkm8R4

Re: A Quick Puzzle to Test Your Problem Solving

#210

Post by ddlutz » Thu, Jul 02, 2015, 9:34 PM UTC

yequalsx wrote: post #136

Math person here. I'm curious to know if anyone used decimal numbers in their tests and if negative numbers were used. The rule is increasing real numbers and one can guess that the rule is increasing numbers without realizing this includes all real numbers and not just integers. In addition to getting it right did you use an exhaustive set of tests?

I tested with real numbers to be curious, just tried 1.1, 1.2, and 1.3.