The foods are cake (C), hamburgers (H), ice cream (I), pizza (P). and sushi (S).
‘Hot foods’ are hamburgers and pizza.
‘Desserts’ are cake and ice cream.
As the game note says, ‘adjacent’ includes diagonals.
1. The only six-letter name is Olivia, so Arlen’s clue tells you that she likes sushi.
2. Olivia tells you that Arlen, Eva, Iris, Olivia, and Upton each have a different favorite food. Since Arlen’s and Olivia’s favorites are known, the remaining three must be some combination of hamburgers, ice cream, and pizza. Arlen also tells you that three-letter names do not like hot foods. This means that Eva must like ice cream.
3. Eva tells you that her diagonal contains one lover of each food. Her diagonal also contains two vowel names: Iris and Upton. According to Olivia’s clue, Iris and Upton like hamburgers and pizza or vice versa. This means that the other two in the diagonal, Queen and Mike, like cake and sushi or vice versa. Olivia also says that Ron is only adjacent to one dessert lover. We just established that either Queen or Mike likes cake, so no one else adjacent to Ron can like cake or ice cream. Since Leo is a three-letter name, we also know from Arlen that he does not like a hot food. Since Leo cannot like either a hot food or a dessert, the only option left for him is sushi.
4. Leo tells you that Gail, Pearl, and Queen all dislike sushi. Based on the work in the previous step, Queen and Mike like cake and sushi; since Queen does not like sushi, she must like cake and Mike must like sushi.
5. Arlen told you that Ron’s favorite food is not hot. Since Mike likes sushi and his clue states that at least three people in that column prefer a hot food, the remaining three in the column- Cici, Heath, and Wendy- all like hamburgers or pizza. Queen’s clue says that someone is only adjacent to cake lovers. Since Leo and Mike both like sushi, everyone adjacent to either of them cannot be the person referred to in Queen’s clue. Since Ron is only adjacent to one dessert lover (Queen), no one else who is adjacent to Ron can like cake; this means that Queen’s clue also cannot refer to anyone in the bottom row. Julie and Tina are both adjacent to a sushi lover (Olivia), so Queen’s clue must refer to someone in the top row. Daisy is adjacent to an ice cream lover, so she won’t work. We know from the beginning of this step that Heath likes pizza or hamburgers, so Brick and Cici cannot be adjacent only to cake lovers either. The only person left is Arlen, so Brick, Frank, and Gail all like cake best.
6. The first half of Frank’s clue tells you that Neal and Kevin cannot like sushi and that they like something different from each other. You also know from Olivia’s clue that Neal does not like a dessert, since Queen does and Ron is adjacent to only one dessert lover. Finally, Gail’s clue tells you that Neal does not like pizza, so Neal must prefer hamburgers.
7. Neal’s clue tells you that, of the three people adjacent to Cici whose favorites have not been revealed yet, one of them is a dessert lover and the other two are non-dessert lovers.We figured out in step 5 that Heath likes a hot food- hamburgers or pizza. You know from Eva that Iris also likes hamburgers or pizza. Since Iris and Heath are non-dessert lovers, Daisy must be a dessert lover. Brick’s clue tells us that two columns contain no female dessert lovers, and only ones left now are columns 1 and 3. (Gail and Queen in column 2 like cake, we just deduced that Daisy in column 4 is a dessert lover, and Eva in column 5 loves ice cream.) This means that Pearl does not like cake or ice cream. She also does not like sushi according to Leo, and she doesn’t like hamburgers according to Queen. Therefore Pearl likes pizza.
8. Arlen and Upton are male, so the ‘girl in the corner’ from Pearl’s clue must be Eva or Zelda. Since Eva tells you that everyone in her diagonal has a different favorite, she cannot have the same favorite as Upton or Iris; Pearl’s clue must refer to Zelda, who must have the same favorite as either Iris or Upton. We know from step 3 that Iris and Upton like hamburgers and pizza or vice versa (reinforced by the fact that those are now the only two foods left for the last two people in this diagonal), so Zelda must also like one of those. Frank tells you that Zelda does not like what Neal likes; Neal likes hamburgers, so Zelda must like pizza.
9. Zelda tells you that her column is the most diverse, with one lover of each food; ever other column must have at least one repeated favorite, and Julie and Tina must love the two remaining foods- cake and hamburgers. Mike says there are six cake lovers in total; five have been revealed, so the sixth and final one is Julie or Tina. In step 7, we established that Daisy is a dessert lover. Since we cannot have more than six cake lovers, Daisy’s favorite must be ice cream.
10. Daisy’s clue tells us that Daisy, Wendy, and Yoda all dislike pizza. We know from step 5 that Wendy likes a hot food; since it’s not pizza, Wendy likes hamburgers.
11. Wendy’s clue is really saying that Heath and Iris have the same favorite food. Upton and Iris are both in Eva’s diagonal and they both have vowel names, both of which mean they cannot have the same favorite. We determined in step 3 that Upton and Iris like hamburgers and pizza or vice versa- both hot foods. Mike tells you that Heath likes a hot food as well, so Heath, Iris, and Upton each like either hamburger or pizza. Wendy tells you that Upton and Heath have different favorites, and we already know that Upton and Iris have different favorites. If Upton is different from both Heath and Iris and all three of them only have two options, Heath and Iris must be the same.
Since Julie must like hamburgers or cake (from Zelda’s clue) Heath and Iris cannot both like hamburgers. Otherwise that row would not have three different favorites (required by Frank’s clue). So Heath and Iris must like pizza and Upton must like hamburgers. Once you know that Heath and Iris have the same favorite, Julie cannot like cake; if she did, that row would not have three different favorites. Julie must like hamburgers. That leaves Tina asthe last cake lover.
12. Since no two of Tina’s currently-revealed adjacents like the same food, she is telling you that Selfi and Yoda have the same favorite, and it must be either hamburgers, pizza, or sushi. But Daisy told you that Yoda does not like pizza, so Selfi and Yoda must both like either hamburgers or sushi. Upton’s clue says that Vance likes pizza OR the same thing as Selfi. Each row needs at least three different favorites (Frank’s clue), so if Vance likes pizza, Selfi and Yoda both have to like sushi. If Vance likes the same thing as Selfi (and therefore also Yoda), all three could be hamburgers or sushi. If all three liked hamburgers, the bottom row would have four hamburger lovers and wouldn’t have enough different favorites. Regardless of whether Vance likes pizza or the same thing as Selfi, Selfi and Yoda must both like sushi.
13. Selfi tells you that every column also has at least three different favorite foods. This mean’s Vance’s favorite is not cake or sushi. Upton said that Vance either likes the same thing as Selfi (which we know is sushi) or pizza, so Vance must like pizza.
14. Right now you know of two ice cream lovers: Daisy and Eva. So Vance is saying that if Cici likes pizza, both Ron and Kevin must like ice cream, since there would have to be four ice cream lovers in total. Julie’s clue says that only one person is adjacent to exactly one lover of each food. That person must be adjacent to exactly five people, so it must be someone on the outer edge but NOT in a corner. Of those twelve people, no one is already adjacent to exactly one lover of each food, but there are two possibilities: Pearl (if Kevin likes ice cream) and Yoda (if Ron likes ice cream). So if Ron and Kevin BOTH like ice cream, then there would be TWO people who are adjacent to exactly one lover of each food. Julie says there is only one such person. Since Ron and Kevin cannot both like ice cream, there can only be three total ice cream lovers. This means Cici’s row cannot contain exactly half the ice cream lovers, and Cici cannot like pizza. We established in step 5 that Cici does like a hot food, so she must like hamburgers.
15. Either Kevin OR Ron must like ice cream, according to Julie. Kevin cannot like sushi, according to Frank’s clue. Since right now only Ron is adjacent to four sushi lovers, there must be one other sushi lover. If it can’t be Kevin, it must be Ron. With Ron as a sushi lover, both Selfi and Neal are now adjacent to four sushi lovers, making Cici’s clue true.
16. No one satisfies Julie’s clue yet, so Kevin must like ice cream, making Pearl the only one adjacent to exactly one lover of each food.