Section 4 Logic Games Questions 1 6 There aren t too many deductions we can make in this game, and it s best to just note how the rules interact and save your time for answering the questions. 1. Type of Question: Global List a) Eliminated by rule #3: G and R can t both give a final argument. b) Eliminated by rule #2: L must prepare an opening argument. c) Eliminated by rule #1: M must be with G or V. e) Eliminated by rule #3: G or R must give a final argument. 2. Type of Question: Local Could Be True If we set up the information we re given, we can fill in 3 of the 6 blanks. It s also clear that R must be in the opening position of the last team, since we can t have both G and R in the final position. This leaves with only two blanks spaces: OPEN: M L R FIN: G a) L and V could be together, but V would have to give the final in order for rule #2 to be satisfied. b) R and S could be together, but S would have to give the final in order for rule #3 to be satisfied. c) This is the correct answer, and the set-up would like this: OPEN: M L R FIN: G V S d) S and V could not be together, as per our set-up. e) S and V could not be together, as per our set-up. 3. Type of Question: Global Could Be True We can approach this question using a combination of rule sweeping and past work. a) This is the correct answer, and the set-up could look like this: OPEN: R L M FIN: G S V b) We can t put G and V together (rule #1) since one of them needs to be with M. c) This would force L into the final argument, violating rule #2. d) This violates rule #1. e) This violates rule #1. 4. Type of Question: Local Fully Determined
Since rule #1 tells us that M needs to be with G or V, and V is now taken, we know that the three groups with be RV, MG, and LS. We know that L must be in the opening position, so S will be in the final. The other four cannot be pinned down to a specific position. b) This is the correct answer. 5. Type of Question: Local Must Be True If L and R are together, we know that L will be in the opening position (rule #2) and so R is in closing. We can t know for sure the way the other groups will play out, but since G and R can t both be in the final position (rule #3), G will have to be in the opening. Our diagram looks like this: OPEN: L G _ FIN: R a) This could be true, but doesn t have to be (V could be on the same team as G). b) This could be true, but doesn t have to be (M could be on the same team as S). c) This could be true, but doesn t have to be (M could be on the same team as S). d) This could be true, but doesn t have to be (V could be on the same team as S). e) This is the correct answer. G must be in the opening position so as not to violate rule #3. 6. Type of Question: Local Could Be True This information tells us that L and S take up two of the opening spots. In order to satisfy rule #1, we ll have to put M on the last team. He ll have to be partnered with G in the opening position, in order to satisfy rule #3 and avoid having both R and G in the final position. OPEN: L S G FIN: M a) This isn t possible. b) This isn t possible. c) This is the correct answer. It could look like this: OPEN: L S G FIN: V R M d) This isn t possible. e) This isn t possible. Question 7 12 This is another game when there are not too many deductions we can make, precisely because we don t know the number of emails actually received. This game hinges on the particular elements of each question, and so it s easiest to just set up and move on to them. It s also good to remember that we ll have either 4, 5, or 6 message (since there are 3 people, and one has to go twice.) 7. Type of Question: Global List a) Eliminated by rule #3: HJ only once b) Eliminated by rule #3: must have HJ once
c) Eliminated by rule #2: first and last message must be by same person e) Eliminated by rule #4: one in first three from J 8. Type of Question: Global Numbers J must fall somewhere in the first three, and since we can t make H last (first = last, and we must have one HJ chain), we can make her second last. This means L will fall twice between J and H: J L L H J c) This is the correct answer. 9. Type of Question: Local Must Be True Since L can t be in position 1, the first and last must be occupied by either H or J. Once we slot in our single HJ chain, we get two options: H J L H or J L H J a) This is the correct answer she can t be in first/last based on rule #1, so she can only occur once. b) This is possible, but doesn t have to be true (H J L H). c) This is possible, but doesn t have to be true (H J L H). d) This is not possible. e) This is possible, but doesn t have to be true (H J L H). 10. Type of Question: Global Cannot Be True L can t be first, and so can t be last. The only way we could know when L can t for sure be is in position 1, and in position 6 if it exists. If we re given any other position, we can t be sure if it will be the last position or not. e) This is the correct answer. 11. Type of Question: Local Must Be True Putting L in 5 limits who can take the 1/6 positions. Since we need an HJ, we can t put J in the 1/6 (J _ L J) because it would block us from putting in HJ. That means we need H in 1 and 6, and J in 2 to make HJ. Since we can only have J in the first three spots once, he ll have to go in 4, with L in 3: H J L J L H a) This is not possible. b) This is not possible. c) This is not possible. e) This is not possible. 12. Type of Question: Local Numbers In order to maximize the distance between Ls, we should choose a diagram with six messages (remember, we re maximizing.) L can t be in 1 or in 6, so the furthest apart she could be in 2 and 5: _ L L _
But this doesn t work either, since this would stop the HJ block from happening (just try cycling H or J into those end spots). So, she ll only be able to have to one spot in between her messages. We saw this is question 11, so here s a hypothetical set-up for it: H J L - J L H b) This is the correct answer. Questions 13 18 This is a pure sequencing game, where all the rules are relative to one another. For these kinds of games, it s best to make a chain, and this game s looks something like this: When making chains like this, it s always important to step make and make sure you know exactly where the entities fall. In this game, only F or R could come first, and only T or H could be last. 13. Type of Question: Global List a) Eliminated by rule #3: R must come before T b) Eliminated by rule #4: S must come before H c) Eliminated by rule #1: F must come before G e) Eliminated by rule #5: G must come before T. 14. Type of Question: Local Could Be True Since we know from our diagram that only R or F can be first, putting F in 3 forces R into 1. G, T, and H can t be in 2 because they require more than R to come before them, so S has to be in the second spot: R S F a) This cannot be true. b) This is the correct answer, and the diagram would look like this: R S F H G T c) R must be ranked first. d) S must be ranked second. e) This cannot be true, since T requires G to come before it. 15. Type of Question: Global Cannot Be True We can approach this simply by counting the entities in the chain. R needs at least three spaces after it, because T, S, and H all must come after R. Since there are only six spots, the latest R could come is in 3. c) This is the correct answer.
16. Type of Question: Global Fully Determined For this type of question, we ll need to find the position that fully determines the rankings. These questions require working through each answer choice, and abandoning them when we don t see anything forming. a) If we put G in 4, we know that F, R, and S will come before it, and T and H after, but we don t know what order these will be in. b) This tells us that T will be in 6, but not much else. c) This is the correct answer. If H is in third, then R and S must come in 1 and 2, and we re left with F, G, and T, which must come in the order F-G-T. We get R S H F G H d) As in question 14, all this yield is R S F _ e) Putting S in 3 means that F and R come before it, and G, T, H after, but the order can t be determined. 17. Type of Question: Local Could Be True The night-shift crew is either G and T or S and H, and drawing a diagram of each doesn t really yield much of anything, so we ll have to just go to the answer choices. a) This would mean S H fill 5 and 6. It won t work, because putting G in 4 means that there isn t any room for T to come after G. b) If we use S and H in 5 and 6, H has to be in 6 because of our chain. c) This is the correct answer if G T is our night shift: F G R T S H d) If we do this, 4 6 read S G T, and this doesn t work, because there s nowhere for H to come after S. e) If we use G and T in 5 and 6, T has to be in 6 because of our chain. 18. Type of Question: Global Cannot Be True This question should be approached with past work. We ve seen F, R, H, and G in 3, so we can eliminate a), b), c), and d) on this. All that s left is S and T, and e) gives us T. e) This is the correct answer. Questions 19 23 There aren t a lot of deductions to be made in this game, but it s important to make sure you understand the rules properly to avoid confusion. For example, rule #2 means that R will either leave the van at the M stop, or will leave after the M stop. This game is made up almost entirely of local questions, so there is a lot of plugging into diagrams involved. Be careful! 19. Type of Question: Global List a) Eliminated by rule #4: J is still on at F, so G must still be on at S b) Eliminated by rule #1: L must be in 1 or 2 c) Eliminated by rule #3: V must get off before J d) Eliminated by rule #2: R cannot get off before M
e) This is the correct answer. 20. Type of Question: Local Could Be True We know that J can never be in the first stop, since V needs to leave before her, so we can eliminate anything with J in it. V can always come in the first spot since she has no stipulations other than coming before J, so anything without V can be eliminated. This leaves us with c) G, V and d) G, R, V. It s just a matter of seeing if R can be placed in the first spot or not with a hypothetical: M L F S R V J G This looks fine. So, c) is the correct answer. 21. Type of Question: Local List If F is the first stop, we know that L has to be in the second to satisfy rule #1. J can never come in 1. R must be with or after M, so she can t be in 1 or 2. Since F is the first stop, the condition in rule #4 is activated (J has to be on when it reaches F), so G cannot get off before S, and also can t be first or second. This means V is the only one that can go in 1, and only J can go in 2: F L V J a) G cannot be in 1, so this is out. b) R cannot be in 1, so this is out. c) G cannot be in 2, so this is out. Even without knowing the final two, this is the only answer choice with V J in 1 and 2. e) R cannot be in 2, so this is out. 22. Type of Question: Local Must Be True For this question, we know we ll have to have L and S in some order in stops 1 and 2. G is in 2, and V has to be in 1 (can t have J in 1, and R needs to be with/after M.) S/L L/S M/F F/M V G R/J J/R a) This could be true, but is not necessarily so. b) This could be true, but is not necessarily so. c) This is the correct answer. R leaves at 3 earliest, and S is either 1 or 2. d) This could be true, but is not necessarily so. e) This cannot be true V gets off first, and the first stop will not be M. 23. Type of Question: Local Must Be False G gets off before S, which means that J will get off before F (rule #4). Since V also needs to come before J (rule #3), we have a chain V J F. This means that the earliest F can stop is 3, and the latest V can leave is 2. a) This could be true if we put F in 3, and G exits at 3. b) This could be true if M is in 2 or 3. c) This could be true.
Since V must leave before J, who must leave before F, V can t be around once the van gets to F. e) This could be true, if M is in 1 or 2.