# Math Test Problem Disagreement

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• 02-26-2003
Govtcheez
"At least" how many cookies are left if " they (the cookies) all disappear"? If all the cookies are gone? The answer's 0. If the cookies are "all" gone, there aren't any left.

What a stupid question...
• 02-26-2003
Mister C
orbitz... Wait until you take higher math like abstract algebra... You will probably be all over your instructor then...

Agree trick question..
• 02-26-2003
salvelinus
5. Since "at least one" student took "at least" 5 cookies, 5 is the minimum for that student, and there's no requirement that any other student took any.
0 would only be correct if "left on the table" at the end of the problem statement meant "left after they were all taken". However, "left on the table" is stated at the beginning of the problem, giving greater weight to the probability that that's what is meant by "left on the table". This is the only ambiguity.
• 02-26-2003
orbitz
Ironically, the reason my teacher is sticking to the answer being 69 is because of the 'must'. He says if atleast one person MUST take 5, then that means we are in a situation where everyone else MUST take 4. BUT, unless he provides a solid definition of 'must', then we cannot be sure what definition he is using, and 'must' has a few definitions, which chagne the result of the answer.

This is ironic because my teacher is hanging onto a grammatical point, and completely ignoring all the other grammatical mistakes in the answer.

I think the question was made with good intentions, but is a horrible question, and a trick.

By the way, this question is taken forma Discrete Math 2 test. I mostly enjoy the class because it seems like alot of the questions try to make you think in a more logical way than other math classes I have had. The problem comes into play with questions where the teacher is askign a question in a vague way because they are afraid they are going to give away too much of the answer, but pay the price in the end because their question is actually to vague to answer. And then they cannot see the other interpretation because they are so focused on what they said. It happens to all of us at some time or another.
• 02-26-2003
dP munky
how the hell do you get everyone else HAS to eat 4 cookies? im not seeing it?

this is the absolute worst question, any answer (technically) would be correct because you have to assume on everything
• 02-26-2003
SourceCode
I gotta go with 3. It sounds like a trick question, the first part says.

Some cookies are left on a table in a room with 17 unsupervised Math students, and they (the cookies) all disappear.

They all disappear, so wether one student must take 5 or not is irrelevant imo. There are no cookies left because they all disappear.
• 02-26-2003
salvelinus
Your teacher is wrong. "..at least one student..." means only one student is required in the problem.
• 02-26-2003
*ClownPimp*
This is a basic Pigeonhole Principle problem. There is no trick in this question. The only ambiguity is if "how many cookies were left" meant after they were eaten or before they were eaten. Considering this is a discrete math class and Im sure you guys recently studied the Pigeonhole Principle, it makes the most sense that the question meant before the cookies were eaten.

The correct answer is #1. The question states that the instructor was "absolutely certain that atleast one of those students must have taken 5 or more of the cookies", the only way he could be absolutely certain is if there were enough cookies such that in every possible distribution of the cookies, someone would have at least 5 of them. The amount of cookies required is 4*17+1 to be sure of this.

Think about it this way, say there were 10 cookies. Can you be sure that at least one person had 5 cookies? Of course not. 10 ppl could have had 1. Now consider 20. Still no, since 14 ppl could have had 1 and 3 could have had 2. Continuing on in this pattern you get to 69 and see that no matter how the cookies are arranged, someone MUST have 5.
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• 02-26-2003
dP munky
>>"..at least one student..."

i think that says it all, 5 dude, 5

69 doesnt make sense, what if every kid only had 3? how do you know? you dont, NO FURTHER INFORMATION
• 02-26-2003
nvoigt
Quote:

69 doesnt make sense, what if every kid only had 3? how do you know? you dont, NO FURTHER INFORMATION
If every kid took 3 the instructor could not have been sure. To be sure that one kid took 5 minimum, there must have been 4 for each kid plus one. So even if each kid took only four, to completely disappear it takes one kid to take five ( or more if someone else takes less ).
• 02-26-2003
dP munky
>>one kid took 5 minimum, there must have been 4 for each kid plus one

this is i guess what i dont get then if one kid took 5 minimum, why do any of the other kids have to take any at all
• 02-26-2003
orbitz
I am not debating the Pigeon Hole Principle thinking, I am debating the grammar of the question and the possible interpretations.

Yes we had recently discussed PHP, but I do not think that recent discussion of the PHP is any excuse for asking a badly phrased question. As mathematictions we cannot assume any prior knowledge as to what the question might be asking but need to answer what the question is asking. What a question is asking is based on how it can be interpreted. With a word problem, we are forced to either A) Be as explicit as possible, leaving as little room for other interpretations as possible, or B) Understand that other interpretations rae possible and make room to allow these other interpreations to be correct answers.

I do not see how the asker of this question did A, the question is somewhat ambigious in it's meaning.

If the asker does B, they have to understand that the language is full of these ambiguities. Also, in a college environment, some people are not as familiar with the language due to diversity, and these interpretations should be taken in to consideration. I understand how the PHP thinking process comes about and what quesitont hat is being answered, but what if we take the sentence:

atleast one student must have taken 5 or more cookies.

If we use one possible definition of te word must: To be determined to; have as a fixed resolve.

Does this meaning not give the answer of 5?

Perhaps I am over analysing this whole thing. But I just think the wording of the question ist oo lose and other interpretations need to be acknowledged as correct.
• 02-27-2003
SMurf
(4 * 17) + 1

Perhaps the students were a bunch of nice people and split the last cookie between them?

Mmm, 1/17th of a cookie :p
• 02-27-2003
*ClownPimp*
>Also, in a college environment, some people are not as familiar with the language due to diversity, and these interpretations should be taken in to consideration

I totally agree. Me saying that #2 didnt make sense was based on my understanding of the word "must" in that context. Of course, someone else with less (or more) experience with English may not have seen it the way I did, and the professor should definitely take that into consideration.

dp munky: read my previous post again, I think my explanation is pretty clear.
• 02-28-2003
Silvercord
punch your teacher in the face

EDIT:
and then POOP all over him (or her)
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