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> So this trick isn’t just a neat blog post, but empirically useful, and I’ll probably include it in prompts from now on for these kinds of problems…

Alernative take: this is a very classic problem used to illustrate this kind of System 1 inaccuracy, so by deliberately including words that increase the conditional probability of us looking at a text that includes discussion on System 1 inaccuracies, you have essentially narrowed down the search space for our dear stochastic parrot to those texts that do contain the right answer.

This sounds dismissive, but I don't mean it that way. I'm just saying that "think about human biases" may not be a universally useful cue, it may only work specifically when trying to get the model to look like a discussion on human biases, and the typical sample problems used to illustrate that.

Very much yes to your first sentence, but I don’t think “just plug something into ChatGPT” is a fair summary of your (very interesting) post, so you’re fine with me.

I’ve seen several statements recently, including one in a talk by a Microsoft researcher working with OpenAI, that claim that all the RLHF safety training introduces human biases and makes the models worse at abstract reasoning. I really wonder why a relatively small amount of human feedback has that effect, while training on this gigantic human-written corpus doesn’t seem to introduce the same biases. That hints at something interesting going on.

To human ears, the problem of 3 hens, 3 eggs, 3 days is a simplified and more obvious problem than the original:

"If a hen and a half can lay an egg and a half in a day and a half ..."

But it's the same problem in the same form, and GPT4 nails it without extra goofy prompting like "don't replicate human cognitive biases".

A more interesting question would cross logic with problem solving.

"If a hen and a half can lay an egg and a half in a day and a half, how many hens are needed to fill Yankee Stadium with eggs in a year?"

But GPT4 doesn't have very good intuition on how to estimate the volume of Yankee Stadium:

Yankee Stadium has a seating capacity of approximately 50,000 spectators.

Let's assume each spectator occupies a space of 2 cubic meters (which is a generous estimate, including seating and legroom).

Total volume (approx.) = 50,000 seats × 2 m³/seat = 100,000 m³

We are gonna need to prefix all prompts with "From now on, act without human biases."

With GPT 4 it nailed it on the first try:

>3 hens lay 3 eggs in 3 days. How many eggs do 12 hens give in 12 days?

>Let's break down the given information and solve this problem step by step.

We know that 3 hens lay 3 eggs in 3 days.

First, we'll find out how many eggs 1 hen lays in 3 days. 3 hens lay 3 eggs, so 1 hen lays 1 egg in 3 days.

Now, let's find out how many eggs 1 hen lays in 12 days. In 3 days, 1 hen lays 1 egg, so in 12 days, 1 hen will lay (12 / 3) * 1 = 4 eggs.

Finally, we'll find out how many eggs 12 hens lay in 12 days. If 1 hen lays 4 eggs in 12 days, then 12 hens will lay 12 * 4 = 48 eggs in 12 days.

I love your comment.

I tried GPT-4 via ChatGPT and it nailed it without any prompt engineering.

---

Prompt: 3 hens lay 3 eggs in 3 days. How many eggs do 12 hens give in 12 days?

GPT-4:

Let's first determine how many eggs one hen can lay in 12 days.

We know that 3 hens can lay 3 eggs in 3 days. This means that each hen lays 1 egg in 3 days (3 hens / 3 eggs = 1 hen / 1 egg).

To find out how many eggs one hen can lay in 12 days, we need to multiply the number of eggs laid in 3 days by 4 (since 12 days is 4 times longer than 3 days). So, one hen will lay 1 egg * 4 = 4 eggs in 12 days.

Now, we have 12 hens. To find out how many eggs they can lay in 12 days, we just multiply the number of eggs one hen can lay in 12 days by the number of hens:

12 hens * 4 eggs per hen = 48 eggs in 12 days.

---

To be completely fair, this math problem can be googled, so it is probably in the training set.

Interestingly if you give GPT-4 the problem but append the instruction "answer only, no explanation" it gets it wrong (I got "108" as the answer in that case).

It is fascinating how much it needs to work step by step.

somehow this answer reminded me of the good advice for starting to tighten a nut. first turn left till you feel the nut drop- then turn right. I feel there is a universal lesson here. Maybe going, as the crow flies, directly toward your goal isn’t always best.

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.

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.)

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

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.