Lying Politicians Logic Puzzle Walkthrough

Everyone is either always lying or always telling the truth. If you figure out that one of someone’s statements is a lie, so must the other. If you figure out that one of someone’s statements is true, so must the other. The only two options for each politician are (E)lected and (N)ot elected. One person was elected and 24 were not.

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(2/25) 
Since Aaron is clearly adjacent to Ace, Aaron must be telling the truth. Therefore Ace was not elected and is a liar.

(3/25) 
You know Ace is lying, so nobody whose name ends in E was elected: Allie, Moe, and Sadie.

(6/25) 
If Sadie is telling the truth, then so are Allie and Moe, but Allie says that Sadie and Moe are lying. So there’s no way Sadie is telling the truth. This means that Allie and Moe are not both telling the truth; at least one is a liar. If Moe is lying, that means Allie is telling the truth about Moe and Sadie being liars. If Moe is telling the truth, then Allie is lying about Moe being a liar. So the bottom line is Sadie is definitely lying, and either Moe or Allie is lying. Since one of Moe or Allie must be telling the truth and both are adjacent to Colby, you now know that Tracy is a liar. This means that all the three-letter names are not elected: Ash, Tad, and Ted.

(9/25) 
Since Ace is lying, you know that the bottom row does not have at least two liars. That means it has one or zero. We already know Tracy is a liar, so everyone else in the bottom row is telling the truth. This means, according to Ted, that Andy is indeed not elected and is telling the truth.

(10/25) 
We know Andy is telling the truth. This means that the following were not elected: Clint, Cyndi, and Melly.

(13/25) 
You know that Tad is telling the truth (Ace). Since Andy is telling the truth, Colby and Cyndi must both be liars in order for Ash to be adjacent to at least two liars. So since Cyndi is a liar, then any liar who is adjacent to exactly three liars was not elected. Melly says that Mason is telling the truth. If that were true, then Sadie could not be adjacent to at least two liars, since you know that Tad and Talia are telling the truth. This means Melly is a liar; therefore Mason is also a liar and Cecil is telling the truth. Since Cecil is telling the truth, Candy must be a liar so that Aaron can be adjacent to two liars (Ace and Candy). Not only is Candy a liar, but she is also adjacent to exactly three liars (Ace, Mason, and Melly), so according to liar Cyndi, she did not get elected.

(14/25) 
Candy is a liar, so there cannot be even one column of all liars. Right now you have a confirmed liar in every column except the middle and far right. (Skyla has to be a liar so that Tracy can be adjacent to at least two liars, since Theo is telling the truth.) In the far right column Cyndi, Stacy, and Tracy are liars. Stacy has to be so that Tracy can be adjacent to at least two liars. The thing to see now is that Ash and Moe could both be liars (except now Candy says no), they could both be telling the truth, or one could be lying. If both are telling the truth, then a liar who’s not in the bottom row got elected. If Moe is honest and Ash is lying, then a truthteller who’s not in the bottom row got elected. But if Ash is honest and Moe is lying, then a liar in the bottom row got elected. This cannot be, since you know that Talia and Theo are telling the truth. So since every column has to have at least one truthteller, Moe must be telling the truth. Ash could also be, or he could be lying. Since Moe is telling the truth, Theo and Talia did not get elected.

(16/25) 
Talia is telling the truth, so Mindy was not elected.

Tracy and Skyla have been established as liars. Moe and Theo have been established as honest. Theo now tells you that Missy is a liar. This means Stacy is adjacent to exactly three liars, and since she herself is a liar (so Tracy can be adjacent to at least two), she must not have been elected, according to Cyndi.

(18/25) 
Stacy is a liar, so neither Mason nor Missy was elected.

(20/25) 
Mason is established as a liar (Melly had to be lying) so there is not even one column with only one liar; they all must have two or more. Right now the only column without two or more confirmed liars is the middle column. You do know now that Allie is a liar, since Moe was telling the truth, so the middle column needs at least one more liar. Mindy and Clint are obviously either both lying or both telling the truth. If they are both telling the truth, then Sean must be the second liar in the column. But if that’s the case, Ash would be half honest, half true, because Sean would be elected (Clint telling truth), but liars would not outnumber truthtellers in every column (middle column would have three truthtellers). So Sean cannot be the only other liar besides Allie in the middle column. And since Clint and Mindy have to be the same, both of them must be liars. Since Clint says Sean was elected, you know that Sean was not elected.

Now that there are at least three liars in the middle column, you know that Ash is telling the truth because liars outnumber truthtellers in every column (Candy+Mason+Sadie, Ace+Melly+Scott (so that Tad can be adjacent to at least two liars), Allie+Clint+Mindy, Colby+Missy+Skyla, Cyndi+Stacy+Tracy). Since Cecil is telling the truth (Melly), you know he was not elected.

(22/25) 
Since Cecil is telling the truth, Skyla was not elected.

(23/25) 
Skyla is a liar, so she tells you that Colby was not elected.

(24/25) 
So Scott was elected.

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