> 3 hens lay 3 eggs in 3 days. How many eggs do 12 hens give in 12 days?
> [...] When we got to it, everybody shouted "Three!"
I don't see why the "common" wrong answer would be 3. Why would anybody think that? The problem looks like this 3, 3 -> 3
When we see the 12 and 12 the intuitive, common, wrong answer should be 12 eggs.
That's what makes sense IMHO.
> "Ovulation (release of the yolk from the ovary) occurs every 24 – 26 hours regardless of fertilization (so a rooster is not needed). A hen ovulates a new yolk after the previous egg was laid. It takes 26 hours for an egg to fully form (white and shell added), so a hen will lay an egg later and later each day. Eventually the hen will lay too late in a day for ovulation to be signaled. She will then skip a day or more before laying another egg." (UWisconsin Livestock)
So, the 3 hens must have been at the least productive point in their egg-laying cycle over the initial three-day time period... Now if we have the two-hour daily offset, over 12 days, ummm, maybe two or three days skipped per hen? So, ah, 108-120 eggs is what the farmer could expect from the 12 hens?
Another similar riddle goes like:
"If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?"
The correct answer there being "5 minutes", and the intuitive wrong answer being "100" as per your post.
That would make sense as to why the teacher also expected "3", since they should be familiar with the existence of their non-intuitive questions, even if they misremember the specific non-intuition.
I didn't need to resort to pen and paper, but I'm also not in primary school.
3 eggs / 3 chickens / 3 days * 12 chickens * 12 days cancels out to 48 eggs
I am not sure to understand what you mean by "wrong" way, I got the right result through a different reasoning that seems to me based on hen-egg-days.
It takes 3 days for 3 hens to make 3 eggs.
The 3 days time are "fixed", i.e. it takes 3 days for each hen to make its own egg.
The egg production rate is 1/3 egg per day per hen.
So I have 12 hens x 12 days x 1/3 = 144 x 1/3 = 48
You've still got a problem though, now when you ask the reader to verify the rule, you have to explicitly state that they're not trying to verify the first rule.
Thank you for pointing this out.