The 7 variables are listed on the top left. There are three possible "groups" - M, N, and F, which stand for Marinated, Nuked, and Fried, respectively. The setup indicates that exactly one ingredient is marinated with the closed box over "M". It indicates that at least two, and possibly three ingredients are nuked (remember, 4 ingredients in total are required) with two closed boxes and a slot inside parentheses above "N". Finally, it indicates that at most one ingredient is fried with the slot inside parentheses above "F".
The rule concerning onions and garlic not both being nuked at the same time is represented in "1". The rule concerning garlic and ham is represented in "2". The rule which states pepper can only be fried is represented by the "P" with a strikethrough under "M" and "N". The rule which states that rice can only be marinated is represented by the "R" with a strikethrough under "N" and "F". The rule concerning tomatoes and shrimp is represented in "3".
And now for the questions:
1. Setup rule 1 eliminates D; setup rule 2 eliminates B; setup rule 3 eliminates A; the fact that at least two ingredients must be nuked eliminates E. Therefore, the answer is C.
2. If P and R are included, P must be fried (as per game rules) and R must be marinated (also as per game rules). So, exactly two ingredients are nuked. Via setup rule 1, A must be the correct answer choice - O and G cannot both be nuked.
3. If T isn't included, S is also not included via setup rule 3. But S is not an answer choice. That leaves GHOPR, four of which are to be included and one of which must be excluded. Because of setup rule 2, we know OPR must be included, since G and H cannot both be included. So, A and D are the only answer choices to check. If we check A by trying to see if it's possible to include G, we quickly see that it is not. GOPR would force P to be fried, R to be marinated, and thus both G and O to be nuked. That's impossible because of setup rule 1. Therefore, the answer is A.
4. Look at the setup and see what happens if you put H and T in the two boxes over the "Nuked" group. For this question, it pays to scan all the answer choices first. Looking at answer choice D, it is quickly evident that O and P cannot both be prepared in the same manner. Therefore, the answer is D.
5. If fried H is included, G cannot be included via setup rule 2, and P cannot be included since P can only be fried and at most one thing can be fried (remember, the question states that H is fried). Therefore, answers D and E can be eliminated. Answers A, B, and C all include S and O, so there is no sense testing them. Only T and R are worth testing. Testing R means that R is marinated. Two ingredients are nuked. They could be either G and T; S and T; or O and T. Therefore, R being marinated and H being fried does not completely determine the other ingredients to be included. The answer must be B.
6. If fried S is included, then P cannot be included via the setup. That eliminates D. In fact, nothing else can be fried, so that eliminates C. T must be included via setup rule 3, so that eliminates B. That leaves A and E. If you test A by excluding O and R, that means that of GHP, two must be included (remember T must be included). Via setup rule 2, P must be included. But that is impossible since at most one item can be fried and S must be fried according to the question. Therefore A is eliminated and the answer must be E.
7. Looking at the setup, if G and S are both included and prepared in the same manner, then G and S must both be nuked. T must also be included via setup rule 3. H cannot be included via setup rule 2. So, GST are included, and one of OPR is included. If you do a quick diagram, using P produces only one possibility since it must be fried. R produces two possibilities since it must be marinated. O produces three possibilities as it can only be fried or marinated given setup rule 1 and the question-specific requirement that G and S are nuked. Therefore, there are 6 possibilities if G and S are included and prepared in the same manner. The answer must be B.
8. I think this is the most time-consuming question. The wrong answers produce one possible set of ingredients but they also constrict the manner in which the one possible set of ingredients must be prepared. For A, if T and G are not included, S is also not included. HOPR are included and since P and R are so highly restricted via the game rules, H and O must also be restricted to being nuked. A is therefore eliminated. For answer choice B, if P and R are included while T is not, then S is also not included via setup rule 3. P and R are restricted to their usual spots, so two of GHO must be nuked. Really, this is enough information to eliminate B, but via setup rules 1 and 2, there is only one possibility, O and H; B is definitively eliminated. For answer choice C, if G is included and S is included and marinated, then H is not included via setup rule 2, R is not included since R can only be marinated and only one ingredient in the recipe is marinated (remember, the answer choice stipulates that S is marinated). Remember also that the answer choice stipulates that P is not included either. That leaves GSTO, all of which must be included. However, there are two possibilities. Either G and T are nuked while O is fried; or T and O are nuked while G is fried. This means that C is the correct answer. D and E can be checked if you are a masochist, and there is something about C which makes it easy to ignore as the correct answer when you first examine it, so you might actually end up checking D and E (I think it has to do with so much information being packed into answer choice C vs. the question as a whole). However, the fact that the two most highly restricted elements of the game, P and R, are not included should serve as a hint that there is some flexibility left in the preparation (marinated, fried, or nuked) of the one possible set of elements remaining. And that is what the question asks for.
Phew!
