Math Test Problem Disagreement
I had a math test recently and got it back and one of the questions I got wrong but feel that the question can be interpreted in a few ways that make the answers different. I was hoping to get other peoples opinion on this question (and their answer to see if it is anything like mine).
The question is:
Some cookies are left on a table in a room with 17 unsupervised Math students, and they (the cookies) all disappear. If, with no additional information, I am absolutely certain that atleast one of those students must have taken 5 or more of the cookies, how many cookies atleast, were left on the table?
The possible answers that I can see:
(Please try the problem before hand so your answer is not tainted...if you care)
The first 2 answers rely on how you interpret:
1) If you interpret the 'must' to say that the student did not have a choice, then the minimum number of cookies is 69. This is to say, if each person takes an equal amount, except for that 1 person, we have the situation where each of the 17 students get 4 cookies, except for the one person who gets 5 so the answer is 4*17+1, 69. This situation uses the second definition of 'must' on dictionary.com saying: To be compelled, as by a physical necessity or requirement.
I am absolutely certain that atleast one of those students must have taken 5 or more of the cookies
In order for all cookies to be gone, and in order for 1 person to haev been required to take 5 cookies, the answer would be no less than 69 cookies.
2) If you interprete 'atleast one of those students must have taken 4 or more' to say that as a minimum, 1 student took 5 cookies, then the answer becomes 5 or more cookies. This situation uses dictionary.com's 4th definition of 'must': To be determined to; have as a fixed resolve.
1 student is resolved or determined to take 5 cookies, and they are all gone, meaning that the minimum number of cookies is 5.
The final answer relies on the interpretation of the last part of the last sentence.
This part states:
3) Under strict grammar, the answer can be 0. How many cookies were left on the table after they disappeared? None.
how many cookies atleast, were left on the table?
I think that this question is badly phrased and that because we are using a language that is full of ambiguities, the question must be as explict as possible as to not allow for any misunderstanding in what the question is asking. I do not think this question accomplished this.
Any feed back anyone could offer would be much appreciated.