ConwayLife.com

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SOLUTION (SPOILER)

















































haha did you really think I'd not force you to solve it to find a solution

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We know there are at least four people, so the only way Saka can win the election is if three districts vote for him 
and two districts vote for dvgrn. Thus the man with the dog must exist. Since the man with the toad has to be in a 
dvgrn-voting non-orange district, he must be in either the blue or yellow districts. However, he can't be in the blue 
district since the man with the fish has to be above him (which can only be the red district) but that can't happen 
since the toad man is occupying the space immediately below the man with the fish, which we know has to be taken 
by the person with the iguana. So the man with the toad has to be in the yellow district. This leaves only red and blue 
districts for the man with the fish, and then we know that he has to be in the blue district, and the person with the 
iguana has to be in the green district. Now this only leaves the red district for the woman with the cat, and the man 
with the dog must be in the purple district or else dvgrn would have a majority vote. So the pets in each district are:

red (saka) - cat
blue (dvgrn) - fish
green (saka) - iguana
yellow (dvgrn) - toad
purple (saka) - dog
orange (dvgrn) - unoccupied

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Scroll down if you want to read the solution and how I obtained it.




















The man with the toad voted for dvgrn (ironically) by (4) and therefore must live in the blue, yellow, or orange district. He cannot be in the orange district because of (8). The man with the fish must live in the blue, green, or yellow district by (2), and the man with the toad must live in a district below the district that the man with the fish lives in by (4), so the man with the toad cannot live in the blue district. Therefore, the man with the toad must live in the yellow district.
The man with the fish must live in the blue, green, or yellow district by (2). Because the yellow district is taken by the man with the toad, the man with the fish must live in the blue district or the green district. If the man with the fish lived in the green district, the person with the iguana must live in the yellow district by (8), but the yellow district is already taken by the man with the toad, so the man with the fish must live in the blue district, so the man with the iguana must live in the green district by (8).
(7) states that the woman with the cat must live in either the red district or the green district. She cannot live in the green district because that is taken by the man with the iguana, so she must live in the red district.
If the man with the dog does not exist, then the election would have been tied because the woman with the cat and the person with the iguana voted for Saka, and the man with the fish and the man with the toad voted for dvgrn. However, Saka won the election by (3), so the man with the dog must exist and must have voted for Saka. Because the only remaining district that would have voted for Saka is the purple district, the man with the dog must live in the purple district.

Summary:
The red district houses a cat.
The blue district houses a fish.
The green district houses an iguana.
The yellow district houses a toad.
The purple district houses a dog.
The orange district is empty.

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The only person who could be in the red district is the woman with the cat. We will never use this fact again but it means we can ignore her.
The person in the red district votes for Saka, and the person with the toad votes for dvgrn, so they are tied. Since adjacent districts vote for different candidates, the fish and iguana's votes cancel each other out. Both candidates are tied now but Saka won, so the final person (the dog owner) must have voted for him and is therefore in the purple district.
Since the toad is below the fish, he must be somewhere below the blue district (the top unoccupied one) but cannot be in the orange district. The only dvrgn-voting district left is the yellow one.
Since the iguana is directly below the fish, they can only be in the green and blue districts, respectively (no currently unoccupied districts are adjacent to the orange one).
The cat is in the red district, the fish in the blue, iguana in green, toad in yellow, and dog in purple. The orange district had a population of 0 in the 2020 census and thus gets 0 representatives (but 2 senators to be chosen somehow?)