The foods are Cake, Hamburgers, Ice cream, Pizza, and Sushi.
Hot foods are hamburgers and pizza.
Desserts are cake and ice cream.
The icons and placement of the people should help you locate them and determine their gender.
The only six-letter name is Olivia, so Arlen tells you that she likes sushi.
Olivia tells you that the following are all different: Arlen, Eva, Iris, Olivia, and Upton. Since Arlen and Olivia 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.
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 then, 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 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. No hot food + no dessert = sushi, so Leo’s favorite is sushi.
Leo tells you that neither Gail, nor Pearl, nor Queen likes sushi. You had Queen and Mike narrowed down to cake and sushi or vice versa in step 3/25 above. So Mike likes sushi and Queen likes cake.
Arlen told you that Ron does not like a hot food best. Since Mike likes sushi, he is telling you that everyone else in the middle column (Cici, Heath, and Wendy) likes hamburgers or pizza. Now look at Queen’s clue. Somebody is only adjacent to cake lovers. Leo and Mike being in the middle and liking sushi rules out 10 people immediately. Also, since Ron is only adjacent to one dessert lover and that is Queen, you can also rule out the entire bottom row. Basically all that’s left is the top row. Daisy is adjacent to an ice cream lover, so she won’t work. We know that Heath likes pizza or hamburgers (beginning of this step), so Brick and Cici cannot be adjacent only to cake lovers either. The only person who can possibly be adjacent only to cake lovers is Arlen. Therefore Brick, Frank, and Gail all like cake best.
The first half of Frank’s clue tells you that Neal and Kevin do not like sushi, and that they like something different from each other. You also know from Olivia that Neal does not like a dessert, since Queen does. Finally, Gail tells you that Neal does not like pizza, so Neal must prefer hamburgers.
Neal tells you that Cici is adjacent to one more dessert lover and two non-dessert lovers. You know from Mike (and Arlen) that Heath likes a hot food. You know from Eva that Iris also likes hamburgers or pizza. So since those two are non-dessert lovers, Daisy must be a dessert lover. This means, according to Brick, that the two columns with no female dessert lover must be columns 1 and 3. So 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.
Arlen and Upton are male, so “a girl in a corner” must be Eva or Zelda. Since Eva tells you her diagonal is all different, then she must be different from Iris and Upton. So Pearl is saying that either Iris or Upton has the same favorite as Zelda. Again, looking at Eva, we know that Iris and Upton like hamburgers and pizza or vice versa, so Zelda must also like one of those. But Frank tells you that Zelda does not like what Neal likes, which is hamburgers. Therefore Zelda likes pizza.
Zelda tells you that her column is the only column with one lover of each food. (You actually know at this point that no other can have all five). So Julie and Tina are cake and hamburgers or vice versa. Mike says there are six cake lovers, so that last one is Julie or Tina. In step 10/25 above, you established that Daisy is a dessert lover. Now you know it must be ice cream.
The three names that contain ‘Y’ are Daisy, Wendy, and Yoda. None of them likes pizza best. According to Mike + Arlen, Cici, Heath, and Wendy all like a hot food. Therefore Wendy likes hamburgers.
You can get 5 names at this point in a variety of different orders that are all basically the same thing. But you have to realize that Wendy is 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. Either one of those facts means they like hamburgers and pizza or vice versa (Eva’s clue or Olivia’s clue). 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 is not the same as Heath, and you already knew that Upton is not the same as Iris. 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, according to Zelda, Heath and Iris cannot like hamburgers. Otherwise that row would not have three different favorites (Frank’s clue.) So Heath and Iris must like pizza. That, of course, means Upton likes hamburgers. Once you know that Heath and Iris are the same, Julie cannot like cake or that row would not have three different favorites, so Julie must like hamburgers. That, of course, means Tina is the last cake lover.
Since no two of Tina’s adjacents like the same food, she is telling you that Selfi and Yoda have the same favorite, and it must be 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. Now look at Upton’s clue. If Vance likes pizza, then Yoda could not like pizza or hamburgers, since 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 hamburgers, the bottom row would have four hamburger lovers – way too many. So whether Vance likes pizza or the same thing as Selfi, Selfi and Yoda both like sushi.
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 (sushi) or pizza, so Vance likes pizza.
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 total. Now look at Julie’s clue. Only one person is adjacent to exactly one lover of each food. That person must be adjacent to exactly five people then. 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 will be two people who are adjacent to exactly one lover of each food. Julie says there is only one such person. So since Ron and Kevin cannot both like ice cream, there can only be three total ice cream lovers. So Cici’s row cannot contain exactly half the ice cream lovers, meaning Cici does not like pizza. According to Mike (and Arlen), Cici does like a hot food, so she must like hamburgers.
Kevin or Ron must like ice cream, according to Julie. Kevin cannot like sushi, according to Frank. Since right now only Ron is adjacent to four sushi lovers, there must be another sushi lover. If it can’t be Kevin, it must be Ron. And with Ron as a sushi lover, indeed both Selfi and Neal are now adjacent to four sushi lovers, making Cici’s clue true.
No one satisfies Julie’s clue yet, so Kevin must like ice cream, and Pearl is the only one adjacent to exactly one lover of each food.
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