# Second Grade Math Riddles--How would you answer? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [February 17, 2009, 1:30am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214 "2009-02-17T01:30:53Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![belladonna](https://avatars.discourse-cdn.com/v4/letter/b/9fc29f/32.png) [@belladonna](https://boards.straightdope.com/u/belladonna)\ **Post date:** [February 17, 2009, 1:30am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/1 "2009-02-17T01:30:53Z")
So my second grader brought home these 2 riddle-type questions on a math worksheet and I’m soliciting opinions on how others would answer, and why. This was a week ago, they’ve already been answered, turned in, and graded so no one will be helping a seven year old cheat here. However, the answers I insisted he use–which he vehemently protested–ended up being marked wrong. _Aghast_ So now I’m in hot water with the kidlet. I’m not saying what we answered, to prevent muddying the waters, but I’m dying for a little validation here. 1. Mrs. Carter saw some animals in her garden. All of them were chickens except one. All of them were roosters except one. Can you figure out how many animals are in her garden? 2. Mr. Carter had some animals in his pasture. All are cows except two. All are horses except two. All are sheep except two. Can you figure out how many animals are in the pasture? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 17, 2009, 1:32am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/2 "2009-02-17T01:32:06Z")
[spoiler]1. No. Maybe there’s one chicken and one rooster. Or maybe there’s just one cow. 1. No. Maybe there’s a cow, a horse, and a sheep. Or maybe there’s just two chickens.[/spoiler] ---
**Author:** ![mnemosyne](https://avatars.discourse-cdn.com/v4/letter/m/c4cdca/32.png) [@mnemosyne](https://boards.straightdope.com/u/mnemosyne)\ **Post date:** [February 17, 2009, 1:43am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/3 "2009-02-17T01:43:02Z")
[spoiler]Either one of two choices for each question 1a. One animal; not a chicken or a rooster 1b. Two animals, one chicken and one rooster 2a. Two animals, neither of which are cows, horses or sheep 2b. Three animals, one cow, one horse, one sheep My mom taught grade 2, and that’s the kind of “logic” which would have been expected from her class. They aren’t good riddles, but these are 7 year olds… it’s a step towards logical thinking, but not the destination! If you answered either of these choices, and the teacher marked them incorrect, then she’s just grading from a book and not thinking about the work she’s assigning to the kids. [/spoiler] ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 1:50am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/4 "2009-02-17T01:50:07Z")
1. Mrs. Carter saw some animals in her garden. All of them were chickens except one. All of them were roosters except one. Can you figure out how many animals are in her garden? Since all roosters are chickens, there are only two animals – one a rooster (which is a chicken), and one that is not a chicken. 1. Mr. Carter had some animals in his pasture. All are cows except two. All are horses except two. All are sheep except two. Can you figure out how many animals are in the pasture? [/QUOTE] Three animals – one cow (and two not-cows), one horse (and two not-horses), and one sheep (and two not-sheep). ---
**Author:** ![belladonna](https://avatars.discourse-cdn.com/v4/letter/b/9fc29f/32.png) [@belladonna](https://boards.straightdope.com/u/belladonna)\ **Post date:** [February 17, 2009, 1:56am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/5 "2009-02-17T01:56:01Z")
1. Mrs. Carter saw some animal **s** in her garden. Can 1 be a valid answer when it’s worded this way? Am I overthinking it? On preview-- that first answer is great **robardin** –and here I was afraid \*I \*was reading too much into it. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 17, 2009, 1:56am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/6 "2009-02-17T01:56:59Z")
I saw your pre-edit post, **mnemosyne**. But don’t worry; your secret’s safe with me. 🙂 To **belladonna** : 1 can be a valid answer when it’s worded that way. It can also not be. It depends on the conventions one is working with… which have perhaps not been explicitly set. Alas. ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 1:57am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/7 "2009-02-17T01:57:14Z")
> [@mnemosyne](#): > > [spoiler]Either one of two choices for each question > > 1a. One animal; not a chicken or a rooster > 1b. Two animals, one chicken and one rooster > > 2a. Two animals, neither of which are cows, horses or sheep > 2b. Three animals, one cow, one horse, one sheep > [/spoiler] I don’t think some of these fit the puzzle statements: [spoiler] 1a. - There are “some animal_s_”, which is to say, more than one. 2a. - “All are cows, except two” would not admit “none are cows”, at least not by my interpretation of “all” at a second grade level. Even by standard set theory, the null set is an empty set.[/spoiler] ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 17, 2009, 2:02am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/8 "2009-02-17T02:02:34Z")
For your second point, **robardin** : [spoiler]We had a debate on this before: in standard mathematical jargon, if there are precisely two things which aren’t Xs, it is legitimate to say “all are Xs, except for two”, even if there are no Xs. You mention set theory, which is perhaps needlessly obfuscating, but in standard set theoretic jargon, one can say “All Xs have property P” even when the set of Xs is empty. In other contexts, of course, the conventions might be different. Since ordinary language is not so heavily formalized, people have different interpretations of how to interpret it. [(Previous thread on the matter)](http://boards.straightdope.com/sdmb/showthread.php?t=478001)[/spoiler] ---
**Author:** ![SciFiSam](https://avatars.discourse-cdn.com/v4/letter/s/47e85d/32.png) [@SciFiSam](https://boards.straightdope.com/u/SciFiSam)\ **Post date:** [February 17, 2009, 2:03am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/9 "2009-02-17T02:03:45Z")
Hard for second grade! [spoiler]Just take each sentence, take what you know you to be true, then add it up. ``` All of them were chickens except one. ``` =definitely one animal not a chicken; indeterminate number of chickens All of them were roosters except one. = definitely one rooster, which is presumably the aforementioned chicken; we now know that the number of chickens is one. So one rooster plus one something else = two animals. All are cows except two. = one cow (minimum) plus two non-cows ``` All are horses except two, one of which we know is a cow. ``` = One horse (minimum) plus two non-horses ``` All are sheep except two. ``` = One sheep (minimum) plus two non-sheep, one of which we know is a cow, one of which we know is a horse. We also know that it really is just one sheep, since the other lines also say ‘except two.’ = 3 animals. That’d be quite hard for my daughter now, partly because she’s not good at logic, partly because she probably wouldn’t know that a rooster is a chicken. [/spoiler] ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 2:07am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/10 "2009-02-17T02:07:40Z")
1. Mrs. Carter saw some animals in her garden. All of them were chickens except one. All of them were roosters except one. Can you figure out how many animals are in her garden? I first answered: Since all roosters are chickens, there are only two animals – one a rooster (which is a chicken), and one that is not a chicken. On second thought, I think the question is meant to have this answer, but by my logic and given the statement, Since all roosters are chickens, there can be any number of animals of a non-chicken kind (say, geese or ducks) in addition to a single rooster. The statement allows for any number of not-chickens, “except one”, which is a rooster. I think the intended statement was “they’re all roosters, except for one; they’re all hens, except for one”. ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 2:11am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/11 "2009-02-17T02:11:41Z")
> [@Indistinguishable](#): > > For your second point, **robardin** : > … Heh. If there were any forum where this would have spawned its own discussion topic it’d be the SDMB 🙂 But yes, that’s why I caveatted my statement as “at a second grade level”, even without having been a part of that other thread. I can see there’s wiggle room for argument at a somewhat high level, but NOT at a second grade level, IMHO. ---
**Author:** ![SciFiSam](https://avatars.discourse-cdn.com/v4/letter/s/47e85d/32.png) [@SciFiSam](https://boards.straightdope.com/u/SciFiSam)\ **Post date:** [February 17, 2009, 2:12am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/12 "2009-02-17T02:12:01Z")
> [@Indistinguishable](#): > > For your second point, **robardin** : > > [spoiler]We had a debate on this before: in standard mathematical jargon, if there are precisely two things which aren’t Xs, it is legitimate to say “all are Xs, except for two”, even if there are no Xs. You mention set theory, which is perhaps needlessly obfuscating, but in standard set theoretic jargon, one can say “All Xs have property P” even when the set of Xs is empty. In other contexts, of course, the conventions might be different. Since ordinary language is not so heavily formalized, people have different interpretations of how to interpret it. > > [(Previous thread on the matter)](http://boards.straightdope.com/sdmb/showthread.php?t=478001)[/spoiler] That sounds like when people make jokes like ‘everyone in the US is happy with paying more taxes, except for everyone in the US.’ It sounds more like rhetoric than logic. ---
**Author:** ![SciFiSam](https://avatars.discourse-cdn.com/v4/letter/s/47e85d/32.png) [@SciFiSam](https://boards.straightdope.com/u/SciFiSam)\ **Post date:** [February 17, 2009, 2:15am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/13 "2009-02-17T02:15:20Z")
> [@robardin](#): > > 1. Mrs. Carter saw some animals in her garden. > All of them were chickens except one. > All of them were roosters except one. > Can you figure out how many animals are in her garden? > > I first answered: > > Since all roosters are chickens, there are only two animals – one a rooster (which is a chicken), and one that is not a chicken. > > On second thought, I think the question is meant to have this answer, but by my logic and given the statement, > > Since all roosters are chickens, there can be any number of animals of a non-chicken kind (say, geese or ducks) in addition to a single rooster. The statement allows for any number of not-chickens, “except one”, which is a rooster. > > I think the intended statement was “they’re all roosters, except for one; they’re all hens, except for one”. But that ignores the second statement, surely? If they’re all roosters except one, there can only be one non-rooster. I did away with spoilers for ths response, because it would get too much. Everyone’s just going to crtl-a anyway. 😃 ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 17, 2009, 2:16am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/14 "2009-02-17T02:16:28Z")
> [@robardin](#): > > Since all roosters are chickens, there can be any number of animals of a non-chicken kind (say, geese or ducks) in addition to a single rooster. The statement allows for any number of not-chickens, “except one”, which is a rooster. > > I think the intended statement was “they’re all roosters, except for one; they’re all hens, except for one”. You got it backwards. Any number of roosters, plus one not-chicken ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 2:18am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/15 "2009-02-17T02:18:51Z")
> [@Indistinguishable](#): > > I saw your pre-edit post, **mnemosyne**. But don’t worry; your secret’s safe with me. 🙂 > > To **belladonna** : 1 can be a valid answer when it’s worded that way. It can also not be. It depends on the conventions one is working with… which have perhaps not been explicitly set. Alas. One could argue it’s the same convention which would allow the use of “people” in a plural way to include cases of a single person. The difference here though is one is not saying “People are people”, but describing a specific scenario with a plural term (“there are animals…”), which IMHO does NOT admit a single value. Maybe it’s 'cause I’ve done too many crosswords but this is deeply set in my bones. If you state “I saw some animals”, and then end up admitting there had been only one, you are guilty of lying, not of clever trickery. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 17, 2009, 2:21am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/16 "2009-02-17T02:21:29Z")
My wife looked up chicken to make sure they weren’t just female (they aren’t), but she found that roosters are not necessarily chickens, the term can refer to other adult male domestic fowls or various other birds. (I hope **belladonna** ’s kidlet is getting all this.) ---
**Author:** ![Leaper](https://avatars.discourse-cdn.com/v4/letter/l/4bbf92/32.png) [@Leaper](https://boards.straightdope.com/u/Leaper)\ **Post date:** [February 17, 2009, 2:23am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/17 "2009-02-17T02:23:07Z")
> [@Indistinguishable](#): > > For your second point, **robardin** : > > _ **points about “standard mathematical jargon” and “set theory” deleted** _ Frankly, I don’t think such things matter to a second grade teacher, or to second graders for that matter. I think, at least when looking for the _intended_ replies, that the simpler the interpretation of the wording is, the better. These things weren’t written with trick-minded adults in mind, after all. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 17, 2009, 2:24am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/18 "2009-02-17T02:24:55Z")
Well, I have tried to, at all times, point out just how sensitive one needs to be to the linguistic conventions set by the particular context, which, unfortunately, may not actually be unambiguous. Still, I had to explicitly mention the conventions of mathematics and set theory because it was going to happen eventually (particularly because, hey, **robardin** did it first. :)). I think it’s entirely reasonable to worry about the ambiguity here, even for second-graders, incidentally; I don’t think they will slavishly fall one way or another as to whether “there are two pigs” and “there’s a cow, a horse, and a sheep” count for the second problem. ---
**Author:** ![SciFiSam](https://avatars.discourse-cdn.com/v4/letter/s/47e85d/32.png) [@SciFiSam](https://boards.straightdope.com/u/SciFiSam)\ **Post date:** [February 17, 2009, 2:29am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/19 "2009-02-17T02:29:02Z")
> [@ZenBeam](#): > > My wife looked up chicken to make sure they weren’t just female (they aren’t), but she found that roosters are not necessarily chickens, the term can refer to other adult male domestic fowls or various other birds. > > (I hope **belladonna** ’s kidlet is getting all this.) Ooh, that does make matters different. Then it’s one rooster plus indeterminate chickens. ‘How many animal **s**?’ equalling less than a plural number might teach kids set theory, but would mess them up when it came to English. ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 17, 2009, 2:29am UTC](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214/20 "2009-02-17T02:29:29Z")
> [@scifisam2009](#): > > But that ignores the second statement, surely? If they’re all roosters except one, there can only be one non-rooster. But if all roosters are chickens, then you’re basically not refining or restricting the first statement with the second with respect to the unknown set of animals. “All are chickens, except one” “All are roosters, except one” (OK, so the chicken’s a rooster) And yes I said it backwards – I meant there could be any number of ROOSTERS and one not-rooster. 1000 roosters and a goose, or 10,000 roosters and a duck, whatever. [Next page](https://boards.straightdope.com/t/second-grade-math-riddles-how-would-you-answer/486214.md?page=2)