I have the feeling here that I may be failing at second-grade logic. 
Perfect opportunity for this anecdote: I was trying to do some maths with my daughter. I asked ‘what’s the sum of 2 and 3?’ Her answer was: ‘a penguin.’ 
Clearly, she was thinking of set theory or something, rather than being distracted by a nearby computer screen. She’s a genius!
That’s true. Doh. I wonder, though, if the teacher was thinking of a rooster and a chicken as not being the same kind of animal, so her answer would be two - a rooster and a chicken. If you phrased it as ‘all are chickens except one,’ and ‘all are geese except one,’ then you’d have a chicken and a goose, yeah?
And then the kids’d start running around playing chicken-chicken-goose.* And making bird noises. This is second grade. Hell, that’d happen with most adult classes!
*I hope you have this game in the US, otherwise that comment will make no sense whatsoever.
A-ha! Two animals: a chicken hen and a rooster of a non-chicken fowl!
We do, except I think it’s more commonly duck-duck-goose around here.
Yes, but the question mentioned chickens.
Whoa, my comment is suddenly quite prescient.
Since, as many people have pointed out, there are multiple options for both q1 and q2, clearly the answer to both questions is “no”. No, you cannot figure out the numbers without further information.
And now that comment doesn’t make sense… (there was editing involved).
Sorry - my computer blurped and did a double post, so I thought it would make sense to edit it to respond to your post instead. I probably should have said so in my edit.
Heh, it’s perfectly alright. I just wanted to clarify my own comment for the benefit of readers who wouldn’t understand.
Now that it’s been hashed out a bit, the answer we used was
Reading through the discussion here I can see where my assumption that the statement “all are cows/chickens/sheep, etc.” means those animals are definitely present in some number was where I went wrong. That makes sense in a way but seems a bit tricky for 2nd graders. Really–on this same worksheet one of the questions was “There are 12 seats around a table, Only 1 seat is empty. How many are filled?” So intricate logic isn’t usually a requirement.
And for the record Aspidistra’s response was the one the teacher was looking for. That being that there was not enough information to answer the question. I spoke with her about it and she claimed that the word “some” was the key. I got hung up on “all”. Ah well, I guess that’ll teach me to second guess a seven-year old
She claimed that the word ‘some’ was the key, but didn’t include the word ‘some’ in her question? Oookaaay.
I still don’t quite understand where you and I went wrong. The question says there’s a sheep, but that doesn’t actually mean there’s a sheep? Huh? Meh. I mean, meeehhhhh. Also: there is no spoon.
Is your son taking a 2nd grade university-level philosophy class or something?
There are two animals in the garden. One rooster (who is both a chicken and a rooster) and one other animal
There are three animals, one cow, one horse and one sheep
On some understandings of the language of the question, it doesn’t actually say there’s a sheep.
Suppose I ran a movie theatre with the policy “All teenagers attending an R-rated film must be accompanied by an adult.”
If it turns out that no teenagers showed up to Sunday’s midnight showing of the latest R-rated blockbuster, have I allowed my policy to be violated?
Not a good analogy. One is making a definitive statement about an existing situation, while the other is posing a hypothetical about a future event.
Let’s make it definite then.
“Every time I’ve ever shown an R-rated movie, all teenagers attending were accompanied by an adult.” says the manager.
“But what about last Sunday’s midnight showing? There weren’t any teenagers!” counters the inspector.
“Yeah, so what? That’s not a counterexample.” retorts the manager.
This is one perfectly reasonable way to use the language of universal quantification. Which isn’t to say it’s the only way; just that it’s a way that exists and is out there.
So now I’m curious - what did your son want to answer when he “vehemently protested” against the answers you put forward?
I think the questions are pretty sucky by the way. Although I maintain that “no” is the answer to the questions as worded, I’d be nervous about answering that on 2nd grade homework for fear of looking like a smartarse.
The construction “Can you figure out…?” is, after all, often used as a polite way of saying “Tell me the answer”. Something like “Is it possible to figure out…?” would have been a lot clearer
But what if there are 8 roosters and one sheep?
All of the animals but one are chickens, (since roosters are chickens) but the one sheep is not.
All of the animales are roosters, but the one sheep is not.
It’s an indeterminate amount of roosters, and one other animal. So, no, not enough info to answer the question.
The second part is the same conclusion I came to.
Upon preview, I see this has been mentioned upthread.
Fine, if the questions had been ‘Mrs Carter often sees animals in her garden. Sometimes she sees [chicken, dodos]. What did she see on this occasion?’ Or ‘Mr. Carter usually has some animals in his pasture. Sometimes he has [sheep, giraffes, etc]. What did he have on this occasion?’
But it was Mrs Carter saw, and Mr Carter had. Those are specific occasions. That would be like asking whether there were teenagers at that r-rated movie last Sunday, not making a general statement about teenagers at r-rated movies.
It’s not asking about every time, it’s asking about one time.
(‘Mr Carter had’ could be ‘used to have,’ to be fair, but then it goes on to say ‘all are …’ implying that whatever he had then, he still has now).
Replace ‘chickens’ with ‘teenagers’ and ‘roosters’ with ‘adults,’ as well as replacing ‘garden’ with ‘cinema,’ and ‘animals’ with ‘people,’ and you have:
Mrs. Carter saw some people at the cinema.
All of them were teenagers except one.
All of them were adults except one.
Can you figure out how many people are in the cinema?
That says to me that there were teenagers and adults there.
Unless it’s based on the word ‘are’ in the last part of the question, in which case it would be a question designed to pick out who is the biggest pedant. Aha! You said ‘are!’ There could be millions of them NOW! Ahahahaha! I’m so clever.
And then the second question has ‘are’ in the main part of the question too, so even pedantry doesn’t win:
Mr. Carter had some people in his cinema.
All are teenagers except two.
All are adults except two.
All are babies except two.
Can you figure out how many people are in the cinema?
I guess you could claim that the occasion that Mr Carter had people in his cinema was a different occasion to the one we’re talking about now, but that really wouldn’t make any sense - you would have mentioned it.
I’m not saying you can’t interpret things your way. I’m just saying, for many people, it’s natural to instead interpret statements about “all Xes” as not automatically carrying the implicit assumption that there are any Xes. We have two possible interpretations here, and natural language isn’t nearly so formalized as to allow us to say one or the other of those interpretations is wrong; they’re just different. There’s ambiguity here.