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Comment by still_grokking | Hacker News Reader

I didn't know this "puzzle" until just now.

Stupid question: What is the "tricky" part about it? How can someone who isn't completely retarded get this even wrong?

This puzzle is trivial, and especially doesn't require any kind of "thinking around the corner". So what is this about?

That language models can't do math (or logic) and can't even reliably tell which of two given written out numbers is the bigger one is imho a different story.

Language models are great for text. But when you need a tool for math and/or logic you should use an adequate tool. We have for example algebra systems for that. Or prove assistants. Or just good old Prolog. It makes no sense to use the wrong tool and than wonder that the results are terribly wrong.

But for the above "puzzle" you don't even need a calculator. So I really don't get the point.

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The trickiness is that it was a part of a set of easy questions. You have 3 same numbers x x x, then change two of them, and ask what's the third y y ? It seems obvious it's y again.

Of course if you have some experience with math (apparently more experience than kids in school have), it's immediately apparent it's a multiplication and the product doesn't scale linearly… But I can imagine myself still answering this incorrectly just because I have no incentive to be careful and I'm in a state of mind to just answer the question quickly. Though while reading the article I solved it, in memory.

> The trickiness is that it was a part of a set of easy questions. You have 3 same numbers x x x, then change two of them, and ask what's the third y y ? It seems obvious it's y again.

OK… That's all?

I start to see the problem.

But I'm not going to write what my conclusion is as this would get likely down-voted into oblivion. (I was actually expecting down-votes already just for asking but still wanted to understand what the issues here is as I honestly don't see any "tricky part" in the "puzzle" at all.)

It is tricky because humans are biased for intuitive understanding rather than logical understanding. Intuitions are shortcuts that are very valuable, but sometimes they are just plainly wrong. Many people will try to apply intuition rather than logic because that works with many other similarly worded questions.

Still don't get it.

The imho intuitive answer is the right one.

I really tried to get what could be tricky about this question. But there is just nothing.

I have no clue how anybody could arrive at anything else[†] than 48. It's trivial. There is no "puzzle" at all.

† (As long as you don't consider RL biology, as than then there is no definite answer, only some probability.)

For a 10 year old.

I would expect every not retarded 10 year old to give the correct answer.

We're talking here about third or forth graders. Those kids should be able to do basic arithmetic with small numbers.

I think it is an issue of language "3 hens lay 3 eggs in 3 days" can be interpreted (as intended that each hen lays an egg only once every three days) or as implying that it is implied that they mean 3 eggs for each hen over the three days, meaning 1 egg per hen per day (incidentally closer to what actual commercial hens lay, not that this matters).

OK, maybe this is something that seems confusing for native English speakers (even I think it should not).

But your interpretation would be correctly worded as "3 hens lay each 3 eggs in 3 days".

"3 hens lay 3 eggs in 3 days" means imho completely unambiguously that "one hen lays one egg every three days".

In practice "each" is optional if it seems implied from context. I mean, if you say "Our employees work 40 hours/week" it would really be weird to interpret it as anything other than each employee working 40 hours a week rather than all employees teaming up to work 40 hours in total. Same thing with hens teaming up to lay 3 eggs. If you mean that hens lay an egg once every three days then say that and the whole thing is far clearer.

Thanks!

This finally makes sense.

Your example nails it. Now I get where the confusion comes form.

I'm not a native speaker and I guess it's not intuitive for me to insert an implicit "each" into the "puzzle" sentence. For me it sounded completely unambiguous. But if you subtextual "hear" an "each" in this sentence the wrong calculations start to make sense.

I've just tried to translate all the variants of the sentences into German (my primary langue) and indeed you would need a "jeweils" in both cases to be clear that you really mean "each". Your example with the employees would sound quite "unclean" without the "jeweils". One would understand it, but it sounds a bit wrong. But in English "Our employees work 40 hours/week" sounds just fine (at least for me).

I guess when I do calculations and "puzzles" in my head I do it in German… :-)

Sapir-Whorf to the rescue! :D

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