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# Stuck on a counting question, would like some help (Sixth Form Difficulty) watch

1. In a multiple choice test, there are four problems. For each problem, there are choices A, B and C. For any three students who took the test, there exists a problem the three students selected different answers for. Determine the maximum number of students who took the test.

I've been at this problem for a bit now still no clue what to do any help?
2. (Original post by imsoanonymous123)
In a multiple choice test, there are four problems. For each problem, there are choices A, B and C. For any three students who took the test, there exists a problem the three students selected different answers for. Determine the maximum number of students who took the test.

I've been at this problem for a bit now still no clue what to do any help?
This is worth bumping. Come on you bright young things, have a go at this!
3. 3^3 is the total amount of different answers you can get when we look at the first three questions, giving 27 students if there were only three questions in the test (with three possible answers) this is also given that each student answered each question differently.

However, the question states that for the fourth problem, for every three pupils, three of them chose the same answer for the fourth problem.

So now, there are just three choices for the fourth problem, either A, B or C.

So 9 students will choose A,
9 will choose B
9 will choose C

So I'm guessing 27 students must have taken the test.

[but it could be 30]

(I don't do S1 until next year lol)
4. (Original post by PedanticStudent)
3^3 is the total amount of different answers you can get when we look at the first three questions, giving 27 students if there were only three questions in the test (with three possible answers) this is also given that each student answered each question differently.

However, the question states that for the fourth problem, for every three pupils, three of them chose the same answer for the fourth problem.

So now, there are just three choices for the fourth problem, either A, B or C.

So 9 students will choose A,
9 will choose B
9 will choose C

So I'm guessing 27 students must have taken the test.

[but it could be 30]

(I don't do S1 until next year lol)
Sorry but I dont think you understood the question
5. (Original post by imsoanonymous123)
Sorry but I dont think you understood the question
Well surely if it the question was concerning four problems, each of which have three possible answers, and no student gave the same set of answers as anyone else, then there must have been 3^4 students which took the test right?
6. Did you write the question out correctly, I can't make sense of what " there exists a problem the three students selected different answers for." means.

For... For what?

edit: Does it mean, there exists a multiple choice question in which 3 students selected different answers.
7. (Original post by MasonM)
Did you write the question out correctly, I can't make sense of what " there exists a problem the three students selected different answers for." means.

For... For what?
I interpreted that as "There is one question in the test where for every three students, one of those students will pick A, one of them will pick B, and the third student will pick C"
8. (Original post by imsoanonymous123)
In a multiple choice test, there are four problems. For each problem, there are choices A, B and C. For any three students who took the test, there exists a problem the three students selected different answers for. Determine the maximum number of students who took the test.

I've been at this problem for a bit now still no clue what to do any help?
12
9. (Original post by MasonM)
Did you write the question out correctly, I can't make sense of what " there exists a problem the three students selected different answers for." means.

For... For what?

edit: Does it mean, there exists a multiple choice question in which 3 students selected different answers.
(Original post by PedanticStudent)
I interpreted that as "There is one question in the test where for every three students, one of those students will pick A, one of them will pick B, and the third student will pick C"
The question isn't ambiguous, I think you're misunderstanding. It's saying that for any 3 given students, on at least one of the 4 questions, those 3 students selected different answers. This question does not have to be the same for all triplets of students.
10. (Original post by Renzhi10122)
The question isn't ambiguous, I think you're misunderstanding. It's saying that for any 3 given students, on at least one of the 4 questions, those 3 students selected different answers. This question does not have to be the same for all triplets of students.

Yeh i know a math question can't be ambiguous. Dunno why you pointed that out.
11. (Original post by MasonM)
Yeh i know a math question can't be ambiguous. Dunno why you pointed that out.
I was making the point that OP had written out the question correctly, hence, no ambiguity... and I was trying to help you to understand the statement of the problem.
12. (Original post by Renzhi10122)
I was making the point that OP had written out the question correctly, hence, no ambiguity... and I was trying to help you to understand the statement of the problem.
Av him renzhi.
You reckon you can solve this Renzhi?

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13. (Original post by physicsmaths)
Av him renzhi.
You reckon you can solve this Renzhi?

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I've tried it, couldn't solve it... yet
14. (Original post by Renzhi10122)
I've tried it, couldn't solve it... yet
LOL.
I shall PM you mate

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