Game Setup

@Boram, Happy to help. We're told that a store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys three shirts from the store. _ _ _ 1 2 3 Then, we're given the rules. A shirt type consists of both a size and a color. _ _ _ _ _ _ 1 2 3 Casey does not buy two shirts of the same type. 1) No repeats Casey does not buy both a small shirt and a large shirt. 2) S - >/L; L - >/S No small red shirts are available. 3) S - >/R; this means that if S - ->SY or SB No large blue shirts are available. 4) L - >/B; this means that if L - ->LY or LR Now let's see if we can make any further inferences for this game before going to the questions. Because both S and L can only be in two different combinations each, and because S and L can't appear on the board together, we know that there must be at least one M on the board. M _ _ _ _ _ Let's take a look at the questions now. Question 1 asks us which answer choice must be false. Answer A says two of the shirts that Casey buys are small and two are red. If two of the shirts are small, then we know that SY and SB are on the board. However, this means that there isn't room for two red shirts as well, so this answer cannot be true (it must be false). This is the correct answer choice. Question 2 says if Casey buys a small blue shirt, which answer choice must be false? We know that SB is on the board. We also now know that there ware no Ls on the board because of rule 2. Answer A says Casey buys two blue shirts. This could be true, as Casey could also buy a medium blue shirt, and this wouldn't violate any rules. This answer is out. Answer B says Casey buys two red shirts. If we have SB on the board, then we know that we cannot have any large shirts on the board. We also know that there are no small red shirts available, so this means if there are two red shirts, then they both have to be medium red shirts. However, this would violate rule 1 (no repeats), so this answer must be false and is our correct answer choice. Question 3 says if Casey does not buy a medium yellow shirt, which of the following must be true? Since we know that there has to be at least one medium on the board, we know that there will be either a medium red or medium blue shirt on the board. M _ _ R/B _ _ Now let's look at the answer choices. Answer A says Casey buys either a medium red shirt or a small blue shirt. But this doesn't have to be true. M L L B R Y This game board means that A doesn't have to be true, so we can get rid of it. Answer B says Casey buys either a medium red shirt or a medium blue shirt. This is exactly what we figured out as soon as we were told that Casey doesn't buy a medium yellow shirt. Since at least one medium has to be there, then that one medium has to be either red or blue. This is the correct answer. Question 4 says if Casey buys exactly one medium shirt and does not buy two shirts of the same color, then she cannot buy which one of the following? M_ _ _ _ _ We know red, blue, and yellow are all used. We also know that since there is exactly one M, the other two shirts are either both small or both large. This is because small and large can't both be on the board at the same time. In looking at the colors for S and L, we have SY or SB LY or LR Answer A says a medium red shirt. This would be fine, as we could have M S S R Y B Answer B says a medium yellow shirt. M L L Y Y R or M S S Y Y B This wouldn't work because it would force there to be two yellows and the question says there can't be two shirts with the same color. This is our answer. Question 5 says if neither large red shirts nor small blue shirts are available, which one of the following must Casey buy? /LR and /SB This is quite restrictive. We could have one board with all Ms, or one board with 2 Ms and one S/L slot since S/L can only be one color. M M M _ _ _ M M S/L _ _ Y Answer A says a red shirt. This doesn't have to be true, as in the second board Casey could buy MB and MY M M S/L B Y Y Answer B says a medium yellow shirt. This also doesn't have to be true, as the second board could be M M S/L R B Y Answer C says either a large shirt or a small shirt. This doesn't have to be true, as the first game board shows (all medium shirts). Answer D says either a medium red shirt or a medium blue shirt. Casey must buy one of these. In the first board with all Ms, at least one has to be red or blue. In the second board, because one slot is already filled with S or L and Y, R or B must be paired with M because there cannot be any repeats. Even though we have three colors to choose from for the two M slots, one of these must be either R or B so that there aren't repeats. Even if we put M with Y in the second board, the other M has to be R or B M M S/L R/B Y Y Answer D is our choice for question 5. Does this make sense? Let us know if you have any more questions!

For rule 2, does that mean that she doesn't buy two of the same shirts with the same size AND color? Or does it mean no repeat of colors?

Hi @Julie-V, The first rule tells us that a shirt type consists of both size and colour so the second rule means that she doesn't buy two of the same shirts with the same type (i.e. size AND colour). Hope this helps! Keep up the good work.