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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

#181

Post by crgt »

Retra wrote: post #167
crgt wrote: post #148

Earlier quoted context omitted.

You mean you correctly guessed without testing at all - and got lucky. I'm not sure this is the same thing as 'solving' it.

I "got lucky" in the sense that my experiences have primed me to recognize that particular kind of question. If the article had actually modified the question framing at all, rather than just copying the existing one, it maybe wouldn't have worked that way. It's the same reaction I have to the Monte Hall problem: I don't have to think or be clever to get the right answer. So naturally you couldn't effectively teach m…

The question could have read the exact same way, with a different final rule as the answer. Without testing at all, you wouldn't/couldn't know that...and so you didn't solve it..you just guessed...

Re: A Quick Puzzle to Test Your Problem Solving

#182

Post by the_af »

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,…

It's not ironic. Dijkstra's assertion is, in a convoluted way, related to the main point of the quiz and the article :)

Re: A Quick Puzzle to Test Your Problem Solving

#183

Post by buckbova »

pbnjay wrote: post #154

If anyone's curious about the raw numbers, I found the counts here: http://int.nyt.com/newsgraphics/2015/2015-06-26-rule-guessin... {"count": 27723, "numNo": 0, "share": 0.7716051100782098} {"count": 2921, "numNo": 1, "share": 0.08129922903504133} {"count": 1883, "numNo": 2, "share": 0.05240891758746417} {"count": 1285, "numNo": 3, "share": 0.035764980934621056} {"count": 880, "numNo": 4, "share": 0.02449274958946811…

Interesting totals. I had 4 No's and would have had at least 5 had I considered negative digits.

Re: A Quick Puzzle to Test Your Problem Solving

#184

Post by jrapdx3 »

joezydeco wrote: post #120
diminishedprime wrote: post #59

Earlier quoted context omitted.

That's exactly what I was thinking. I (sometimes) follow TDD, and I applied it to this problem. I made sure to include negatives, 0, positives, and include primes here or there to help avoid issues with multiplication/exponentiation. After a few of these, I felt pretty confident that the rule was simple.

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

Yes I did, though not to 28 places as tptacek had done. With 2 to 4 place floats, including negatives, the test worked as expected.

Like others here have said it wasn't a particularly hard "rule" to figure out. Easy to immediately rule out geometric relationship as in 2^y, which didn't leave a whole lot of possibilities to test. For the commenters here, I'd attribute ease of finding the solution to familiarity with the kinds of problems that programming presents.

Which leads to the idea there's value in learning even the rudiments of programming. Logically, it should encourage better problem-solving skills in general. We might think there this has important implications for our educational systems. But I know, that's probably not realistic at all.

Re: A Quick Puzzle to Test Your Problem Solving

#185

Post by thaumasiotes »

Sadgrinner wrote: post #157
dude_abides wrote: post #116

I'm a data scientist, and it relieved me no end that I got this one right: http://i.imgur.com/V5oJ4i4.png I would have had second thoughts about my career choice if I got this wrong :) The correct approach for any data modeling problem is to think in terms of entropy. Each subsequent approach should minimize entropy, until you reach diminishing returns.

Isn't your answer technically wrong, though? The sequence is not monotonically increasing. It's strictly increasing. If you test [1, 1, 2] or [1, 1, 1] or [1, 2, 2], you'll get "No" answers even though those sequences are monotonically increasing.

Not so.

http://mathworld.wolfram.com/MonotoneIncreasing.html

Re: A Quick Puzzle to Test Your Problem Solving

#186

Post by [deleted] »

sp332 wrote: post #53
EvanKelly wrote: post #47

Earlier quoted context omitted.

I'm curious about how you came to your answer and what led you there? Were you testing a pre-supposed hypothesis that confirmed itself?

I got the part about increasing eventually, but I thought the third number also had to be the sum of the other two. I came up with the sum idea after trying (3 6 9), so only 2 tests. The idea that they had to be increasing came later. I don't have it open but I'm pretty sure one of my tests was (1 2 5) which should have tipped me off... in conclusion yes, I'm probably dumb.

[deleted]

Re: A Quick Puzzle to Test Your Problem Solving

#187

Post by carussell »

snowwrestler wrote: post #113
sp332 wrote: post #53

Earlier quoted context omitted.

I got the part about increasing eventually, but I thought the third number also had to be the sum of the other two. I came up with the sum idea after trying (3 6 9), so only 2 tests. The idea that they had to be increasing came later. I don't have it open but I'm pretty sure one of my tests was (1 2 5) which should have tipped me off... in conclusion yes, I'm probably dumb.

I know you're joking, but I think this is important: Failing the test does NOT mean a person is dumb. The point of the article is that confirmation bias seems to be a fundamental default in the way everyone thinks. Certain people with specialized training in inductive problem solving (scientists etc.) have learned to compensate. If folks think it's an issue of intelligence, then they might be willing to think "but no…

I wonder how much games like Twenty Questions plays into conditioning towards this kind of approach, since the implication there tends to be that the fewer questions you ask, then the better you've done.

Re: A Quick Puzzle to Test Your Problem Solving

#188

Post by graycat »

16bytes wrote: post #162
graycat wrote: post #90

Typical NYT psycho-babble: I got the right answer but with several Yes answers and also several No answers and without their confirmation bias and other nonsense. And, I do know about "problem solving", thank you, with some of my solutions responsible for my peer-reviewed published papers and Ph.D. in some STEM work at a world class research university. Sorry, NYT: I don't regard your organization as able to "test" "…

Have you considered that you missed the point entirely? It's hard to see how you consider this an insult and not an interesting "live" experimental result. "Test your problem solving skills" is merely the experimental set-up and the purpose isn't to actually measure problem solving skill, but rather to demonstrate confirmation bias on a population. Your alligator tears and perceived insult add nothing to the conversa…

"Interesting"? Not at all. Instead, sick-o.

> demonstrate confirmation bias

Nonsense. Psycho-babble. Got to be total mush-brained to have that exercise cause "confirmation bias".

Indeed, elsewhere in this thread are descriptions of some quite careful work with that puzzle with no hint at all about "confirmation bias". Again, that that "test" illustrates the psycho-babble of "confirmation bias" is nonsense -- it illustrates no such thing.

Maybe the "test" caused something like "confirmation bias" in you, although I doubt it. In me it caused no such thing.

Instead all their efforts at hints, distractions, I, of course, deliberately ignored, successfully so. Got to be mush-brained to jump at the first conclusion that the "rule" was about powers of 2 or doubling; instead, make such a conjecture and put in some input to test it. I did that. I'm sure nearly everyone on HN who tried the "test" did that. We're just not going to jump to a conclusion that the rule is about powers of 2 -- no way. "Confirmation bias"? Horse feathers.

> Your alligator tears and perceived insult add nothing to the conversation.

In no way is my post about me.

But somehow the NYT has some very good friends on HN.

Re: A Quick Puzzle to Test Your Problem Solving

#189

Post by the_af »

sp332 wrote: post #53
EvanKelly wrote: post #47

Earlier quoted context omitted.

I'm curious about how you came to your answer and what led you there? Were you testing a pre-supposed hypothesis that confirmed itself?

I got the part about increasing eventually, but I thought the third number also had to be the sum of the other two. I came up with the sum idea after trying (3 6 9), so only 2 tests. The idea that they had to be increasing came later. I don't have it open but I'm pretty sure one of my tests was (1 2 5) which should have tipped me off... in conclusion yes, I'm probably dumb.

Like the other comment said, this is not about being dumb. It's about human psychology: you'd rather not be wrong, so you jump at the possibility of being right, and "forget" to take the logical step of actively trying to disprove your rule (1 2 5 can be disregarded because you weren't trying to disprove the rule).

Re: A Quick Puzzle to Test Your Problem Solving

#190

Post by monjaro »

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...
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