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Many people ask similar questions about the statements of Quiz problems via our QQ helpline. Here are some that your fellow students have already asked; you might find the answers helpful!
What about compound statements?
Questions and statements can be compound (using, e.g., 'and', 'or', 'if'), but an answer will still only have a single truth value. For example, if you asked, "Is Mathcamp awesome, and is the sky green?", the answer would be "no" because only one of the two parts connected by "and" is true.
Does the die have to be 3-dimensional? That is, what numbers of sides, N, are allowed?
Any whole number of sides N > 0 is allowed; the geometry is not relevant. In particular, can you have a die with just two sides (or even one)? Yes, you can, even though this doesn't really make sense physically (they are magic after all!).
Problem 3(c) asks for a maximum, but aren't you allowed to have, say, n2-1 gardens and 1 apartment? (Even though, at that point, it becomes more of a garden complex than an apartment one :) )
You could have a garden in every lot, and you're right that that would be more than (1/5)n2 gardens. But the question is saying the apartment complex can be constructed with no more than (1/5)n2. It wants you to prove that no matter what n is, it is always possible to build an apartment complex with at most that many gardens, while still giving all apartments a scenic view. (As several of you who asked this question have pointed out, it is also possible to build one with many more gardens!)
Do the samples in parts (b) and (c) still have at most 32 people, or may they vary in size?
Yes, the 32 sample limit applies to all parts of the problem. You can have smaller pooled samples but not larger ones.
In parts b and c, does the restriction that only 16 tests are available for the entire town still apply?
No, the 16 test limit is just for part a. (The second paragraph of problem 5 applies to all parts, though: in particular, the at-most-32-samples-per-pooled-sample limit is still true in b and c.)
The problem says: "not only do you not know who is sick, but even how many of the 10 are." Is it saying that we don't know who is sick and we DON'T know how many of the 10 are, or is it saying that we do know who is sick and we DO know how many of the 10 are?
You DON'T know how many of the 10 are. Maybe one of them is sick, or maybe seven are; either way the test result will just say "positive" and you get no further information.
Can two players have the same skill level, so their game is a tie?
No, there cannot be ties. Either A ≺ B or B ≺ A.
In part (b), is the question correct as it is, or should both sequences be of length n?
Yup, it's supposed to be as written: an increasing subsequence of length 3 or a decreasing subsequence of length n.